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Unit 6 Fluids and Pressure • • • • • • • •

What is a fluid? How is pressure defined? Pressure due to liquid and atmosphere What is gauge pressure 計示壓力 and absolute pressure 絕對壓力? How is pressure measured? What is blood pressure, systole 心臟收縮 and diastole 心臟舒張? How is the blood pressure measured? Bernoulli’s principle 伯努利原理 and its applications

1. Fluids and pressure in fluids Fluids include all liquids and gases. Both the human respiratory and circulatory system contain fluids. Atmospheric pressure, hydraulic pressure, and blood pressure are all examples of fluid pressure. 2. Definition of pressure Pressure is the force applied perpendicularly to a surface of area A, and is calculated by the following equation.

pressure =

force F = area A

Pressure is measured in pascals. 1 Pascal is equal to 1 newton per square meter (N/m2). One Pascal is a small pressure. An apple exerts about 1000 Pascals (Pa) on your hand. The greater the area a force is applied to, the smaller the pressure.

3. Liquid pressure 1. Pressure in a liquid increases with because of the greater amount of liquid down.

depth pushing

2. Pressure at a given depth acts equally directions.

in

3. The pressure at a given depth does not on the shape of the vessel containing the It only depends on the depth.

depend liquid.

4. Pressure depends on the density of the The denser the liquid, the greater the pressure at any given depth. .

liquid.

all

Pressure due to the weight of a fluid P = hρg

h is the height of the liquid ρ is the density of the liquid g is the gravitational force (9.8 N/kg) The bottom of this container supports all of the the liquid. The sides of the container do not exert force because it is not possible for shear force to be applied on it.

weight of any upward

4. Atmospheric pressure The atmosphere also exerts fluid pressure on the Earth. Patm is the static pressure exerted on Earth by the atmosphere at sea level. On a windless day, the column of air on 1.00 m2 of Earth at sea level weighs about 1.013x 105 N. Patm = 1 atmospheric pressure (1 atm) = 1.013x 105 N/m2 = 1.013 x 105 Pa Example: At what depth does water exert the same amount of pressure as the entire atmosphere? Calculate the depth at which water exerts pressure equal to 1 atmospheric pressure.  P = hρg

, so h x 1000 kg/m3 x 9.8 N/kg =1.013 x 105 N/m2 h= 10.1 m

5. Gauge Pressure, absolute pressure

The pressure in the blood vessels include the pressure exerted by the blood, and the pressure exerted by the atmosphere. However, only the pressure exerted by the blood matters, since the atmospheric pressure is exerted on the blood going into the heart as well as the blood coming out of the heart. The pressure exerted only on the blood is the gauge pressure (Pg). This pressure is measured relative to the atmospheric pressure (1 atm). This is the pressure that is measured when taking your blood pressure or car tire pressure. The total pressure (pressure of the blood plus the pressure of the atmosphere) is the absolute pressure (Pabs). This pressure is measured relative to a vacuum (0 atm). The total or absolute pressure is equal to the gauge pressure plus the atmospheric pressure. The comparison of two gauge pressures is called relative pressure or differential pressure. Measurements of the pulmonary system 呼吸系統 includes both gauge and relative pressures. The atmospheric pressure is exerted on everything except for things in a rigid air-tight container. This is because of Pascal’s principle. Absolute pressure is equal to gauge pressure plus atmospheric pressure.

Pabs = Pg + Patm • • •

absolute pressure in fluids cannot be negative. the smallest absolute pressure is zero. the smallest possible gauge pressure is Pg = -Patm (i. e. Pabs is zero)

When the absolute pressure of a fluid is less than the value of Patm, its gauge pressure is negative.

6. Measurement of gauge pressure Pascal’s principle 帕斯卡原理: A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. Pascal’s principle is used in remote pressure sensors. The sensor does not have to be contacting the liquid it is measuring because of the undiminished transmission of pressure throughout the fluid. This is useful in measuring blood pressure, since the sensor will not have to contact the blood. In mechanical pressure gauges such as an oil gauge, the pressure of liquid creates a force, converted into a pressure reading.

pressure which is then

Open-tube manometer Manometers (壓力計 ) are used to measure gauge pressure. Manometers rely on the principle pressure of a fluid is P = hρ g

that the

(a) The liquid levels on both sides of the tube are the same. Both sides are open to atmosphere. Therefore atmospheric pressure pushes down on both sides equally. (b) The left side of the tube is open to the atmosphere. Pressure is applied on the right hand side. The positive gauge pressure Pg = hρ g is transmitted to the left hand side of the manometer, supporting liquid column of height h. (c) The pressure applied on the right is less than the atmospheric pressure by hρ g. This is a negative gauge pressure of - hρ g.

Mercury manometer This is a mercury manometer. It is very similar to to measure blood pressure. The left side of the open to the atmosphere. The right side can be atmosphere by a valve to release pressure.

what is used manometer is opened to the

• The gauge pressure can be represented as millimeters of mercury (mmHg). It may be above or below the atmospheric pressure • The reference point of gauge pressure is 1 atm. • Blood pressure measurement are commonly made by the mercury manometer, and values are usually given in mmHg. • When the valve is open, the mercury level on both sides will be the same since there is an equal amount of pressure on the left and right side • If the valve is closed, the pump can increase the pressure in the manometer. The height of the mercury in the left will show how much pressure has been added.

Barometer Mercury barometers ( 氣 壓 計 ) are used to measure atmospheric pressure. As shown in the diagram, the atmospheric pressure is exerted on the mercury open to atmosphere, causing the mercury in the closed tube to There is no pressure in the tube because it is a vacuum. height of the mercury in the closed tube can be used to atmospheric pressure which equals hρ g. 1 atm = 760 mm Hg = 760 Torr = 1.013 x 105 N/m2 (density of mercury: 13.6 x 103 kg/m3)

the rise. The find the (Pa)

7. Blood pressure The left ventricle pumps blood to the arteries (動脈), and causes the pressure in the blood vessels to rise and fall. The blood pressure can be felt on the neck or the inside of the wrist (腕), according to Pascal's principle. Systolic and diastolic blood pressures Systole When the left ventricle contracts, blood in the arteries increases. The aortic valve ( 主 closes when the pressure in the aorta ( 主動脈 ) than the pressure in the heart. This is called The corresponding peak pressure is systolic 收縮壓.

pressure ) is larger systole. pressure 動脈瓣

Diastole The pressure in the aorta then decreases as the blood in it flows to the body. This causes a pressure wave to travel through the arteries that slowly fades. When the pressure in the aorta is less than the pressure in the left ventricle, the aortic valve is forced open. This is diastole. The pressure of the blood when the aortic valve opens is called the diastolic pressure 舒張壓.

8. Measuring blood pressure A common way to measure arterial blood pressure is the auscultatory ( 聽 診 ) method. This method requires a sphygmomanometer (血壓計), which includes of a blood pressure cuff, a hand pump, a mercury manometer, and a stethoscope (聽診器). The cuff used to measure the blood pressure should not be too narrow, or it will falsely raise the blood pressure. The inflatable bladder inside the cuff should have a width that is 40% of the arm circumference, and a length that is 80% of the arm circumference. The stethoscope consists of 4 basic parts: a bell, a diaphragm, tubing, and earpieces. The bell can detect a broad spectrum of sounds and is used to listen to low-pitched heart and lung sounds. The diaphragm is used to listen to high pitched heart and lung sounds. The tubing should be thick enough so that external noise cannot be heard. Fluid flow in a pipe When a fluid is flowing slowly the flow is said to be steady flow 層 流 ). Streamlines, which representing the direction of fluid drawn parallel to the pipe walls.

along a pipe, (laminar are lines flow, are

When the liquid flows faster than a certain speed, the friction between the pipe walls and the liquid increases. This creates turbulence, and the streamlines are no longer straight. This is called turbulent flow (湍流). How to determine systolic and diastolic pressures In normal blood arteries, blood a smooth, laminar flow. Nothing can be heard by the stethoscope in cases.

travels in special these

When measuring blood pressure auscultatory method, the pressure of around the arm increases until the blocks the arterial blood flow.

using the the cuff pressure

The pressure is slowly released until below the systolic pressure. The of the cuff is now slightly below the pressure, but above the diastolic The blood will flow in spurts when pressure is above the cuff pressure, stop when it is below the cuff During this time, the blood flow is turbulent, resulting in audible The Korotkoff sounds ( 柯氏音 ) can during blood flow.

it falls pressure systolic pressure. the blood and will pressure. sound. be heard

There are five types o Korotkoff sound.1 The first Korotkoff sound can be heard when the cuff pressure falls just below the systolic pressure. As the pressure in the cuff is allowed to fall further, thumping sounds continue to be heard as long as the pressure in the cuff is between the systolic and diastolic pressures, as the arterial pressure keeps on rising above and dropping back below the pressure in the cuff. The fifth Korotkoff sound is the silence when the cuff pressure falls below the diastolic pressure. The blood flow has returned to normal and is laminar. Blood pressure is measured in millimetres of mercury (mm Hg), and is shown as systolic pressure over diastolic pressure. For example, 120/80.

9.

1

http://en.wikipedia.org/wiki/Korotkoff_sounds

Bernoulli’s Principle (Optional)

The following equations apply to an incompressible, frictionless, steady flow fluid.

P + 12 ρ v 2 + ρ g h= c o n sorta n t P1 + 12 ρ v12 + ρ g h1 = P2 + 12 ρ v22 + ρ g h2 For h1=h2

P1 + 12 ρ v12 = P2 + 12 ρ v22

We can conclude from the equation that a higher fluid velocity equals lower fluid pressure.

When air flows between two vehicles, it velocity because of the narrower This creates a low pressure between the higher pressure on the outside of the pushes them together.

increases in passageway. vehicles. The vehicles

(a) Thi s

Bunsen burner has an adjustable nozzle used to control the amount of air entering to cause combustion (b) This atomizer uses a squeeze bulb to propel air over perfume so that the perfume can be changed into vapour form (c) This aspirator uses high velocity water to create negative pressure to suck air into a tube. It is used by dentists and surgeons. It is also used to drain flooded basements (d) This water heater uses the movement of hot air to suck cool air into its chimney Check list

After studying this unit you should be able to • • • • • • • • • • • • • • • •

recall fluids and examples of pressure in fluids define pressure and recall its unit recall liquid pressure, connect the pressure in a fluid with its depth and density, P = hρg . recall atmospheric pressure Patm and the following relation for Patm at sea level: Patm = 1 atmospheric pressure (1 atm) = 1.013x 105 N/m2 = 1.013 x 105 Pa recall definition of gauge pressure, absolute pressure, and how they are related, the type of pressure in human systems. Recall pascal ‘s principle, describe how a open-tube manometer may be used to measure gauge pressure. describe the principle of mercury manometer and gauge pressure in mmHg describe the principle of barometer and define the atmospheric pressure in terms of mm Hg height. Explain what is blood pressure, explain systolic pressure and diastolic pressure describe parts of sphygmomanometer describe parts of a stethoscope explain the difference between steady (laminar) and turbulent flow. Explain the measurement of systolic pressure and diastolic pressure Explain the record of a blood pressure measurement: the meaning of the figures. Recall Bernoulli’s principle and its applications

Unit 7 Electricity I 1. Electrostatics 1.1 Electric charge If a glass rod is rubbed with a silk, some electrons are moved from the glass to the silk by friction. So the glass rod becomes positively charged the silk negatively charged. Since the glass and silk have opposite charges, they attract each others. Two such rubbed glass rods will repel one another since each rod has positive charges on it. The phenomenon of attraction or repulsion between charged objects is called electrostatics. above process, no electrons are created or destroyed; they are simply transferred from one object to another, while the total charges are not changed. The rules of electrostatics are: • objects with the same charge repel • objects with opposite charges attract

and

In

Electric charge q has the unit Coulomb in SI unit, abbreviated C. The basic charge of an electron and a proton are identical in magnitude but opposite in sign. The magnitude of this basic charge is: qe =1.6x10-19 C. From above relation: 1 C = 6.25 x 1018 electrons (or protons)

1.2 Electrostatic force The attraction or repulsion forces between charges are called electrostatic force. The direction of the electrostatic force is based on the charge involved. Opposite charges generate an attractive force (the sign is negative); like charges generate a repulsive force (the sign is positive). The magnitude of the force is proportional to the product of q1 and q2 ; and inversely proportional to the square of the distance r. Therefore the electrostatic force: • decreases with distance  increases with quantity of charges

r

q1

r

q2 (a) Opposite charges

q1

q2 (b) like charges

1.2 Charges at work Electrons can be transferred from one object to another by simple touching; this method of charging is called charging by contact. The example of electroscope is an example of charging by contact. An electroscope is made with gold foil leaves hung from a metal stem and is insulated from the air in a glass-walled container. (a) A positively charged glass rod is brought near the electroscope, attracting electrons to the top and leaving a net positive charge on the leaves. Like charges in the light flexible gold leaves repel, separating them. (b) When the rod is touched against the ball, electrons are attracted and transferred, reducing the net charge on the glass rod but leaving the electroscope positively charged. (c) The excess charges are evenly distributed in the stem and leaves of the electroscope once the glass rod is removed.

Substances, such as metals, in which electrons can flow freely, are good conductors. Plastic, polyethylene and rubber conduct badly and are called insulators. Charging by contact is not the only way to transfer excess charges to a metallic object in order to charge it. In this example, (a) Two uncharged neutral metal spheres are in contact with each other but insulated from rest of the world. (b) A positively charged glass rod is brought near the sphere on the left, attracting negative charge and leaving the other sphere positively charged. (c) The spheres are separated before the rod removed, thus separating negative and positively charge. (d) The spheres retain net charges after the inducing rod is removed. This process is called charging by induction.

or the

is

In insulators the charging takes place differently: no free charge flows, a charged object attract an insulator by polarizing its molecules: the center of positive charge and negative charge of a molecules shift slightly: charge polarization.

Negatively charged clouds induce a positive charge on the surface of a building. Lightening strike occurs when there is a sudden discharge between the cloud and the building. The purpose of a lightening rod is to continually collect electrons from air and discharge them, preventing a large buildup of positive charges on the building by induction.

1.3 The electric field

Electric field E defines the electric force exerted on a positive test charge qo positioned within any given space:

r

F E= qo

q

qo

The direction of E depends on the force exerted by the charge q. Since the test charge qo is positive, if the charge q is positive, an repulsive force is generated and the direction of E is away the charge q; if the charge q is negative, an attractive force is generated and the direction of E is toward the q;. Electric field is expressed in SI unit as N/C. Electric field line is used to express directly the direction and the intensity of the electric field E. The arrow points to the direction of the electric field, the number of lines indicates the intensity of the electric field.

+

1.4 The electric potential difference (voltage) A charge accelerated by an electric field is analogous to a mass going down hill. In both cases potential energy is converted to kinetic energy. In the first case; the electric potential energy (EPE) of the charge is converted to kinetic energy of the charge q.

The electric potential difference or voltage, ∆V , is the change of the EPE per unit charge, considering the test charge q moving from A to B, then: ∆V = VB −VA =

EPE B − EPE q

A

or

∆EPE = ∆V ⋅ q

The unit for ∆V is Volt (V). 1V=1 J/C.

1.5 Capacitors A capacitor is a device that can store energy and consists of two oppositely charged conductor plates that are separated by a distance d. The capacitance C is defined as :

C =

q ∆V

where q is the magnitude of charge stored on each plate and ∆V is the potential difference between the two metal plates. (sometimes we use simply V to represent

∆V

).

The SI unit for capacitance is the farad (F), 1 F =1 C/V. The potential energy stored in a capacitor is given by : U =

1 c (∆V ) 2 2

+Q

-Q E

Area A

d

The insulating material inserted between the plates is called a dielectric. The charged plates polarize the molecules in the insulating material between the plates of a capacitor. This produces a layer of opposite charge on the surface of the dielectric that attracts more charge onto the plate, increasing its capacitance. The capacitance a parallel plate capacitor with a dielectric is:

C =

of

κ εo A d

−12 2 2 where ε o = 8.85 × 10 C / N ⋅ m is the permittivity of the free space,

the insulating material, and A is the area of each plate.

κ the dielectric constant of

All living cells are protected from environment by a thin semi-permeable wall called a cell membrane. The membrane possesses channels of pores that allow a selective passage of metabolites and ions in and out of the cell. The thickness of a cell membrane varies between 7nm to 10nm (1nm=10-9m). Membranes act as capacitor maintaining a potential difference between oppositely charged surfaces of inside and out cell. This potential is about 0.1V, giving rise to an electric field of about 10MV/m, a very high electric field. A typical value of the capacitance per unit area C/A is about 1 mF/cm2 for cell membranes. This relates the membrane’s dielectric constant via:

κ

giving a value of Materials: :

κ

C κ oε = A d

κ ≅ 10 for membrane. Here is some dielectric constants of various dielectrics:

Air 1

Pyrex mica 4.7 5.4

Silicon 12

Ethanol 25

water 80

BaTiO3 7000

2. Electric current 2.1 Charge flow A charged particle is accelerated in a electric field. The flow of electric charges in a conductor is called electric current. The flow of charges is caused uniquely by the electric potential difference (or voltage) at the two ends of the conducting wire. A positive charge accelerates from a region of higher electric potential to a region of lower potential; a negative charge accelerates from a region of lower potential to a region of higher potential. To sustain such flow of charge, a special device must be provided to maintain the voltage. The situation is analogue to the flow of water from a higher reservoir to a lower one. The simplest “pumping” device which provides such voltage is a battery.

The current I is given by:

I =

∆q ∆t

where ∆ q is the magnetite of the charge crossing a surface in a time ∆ t, the surface being perpendicular to the motion of charge. The SI unit of current is ampere (A), 1 A= 1 C/s. In a circuit of metal wires, electrons make-up the flow of charge. These electrons are called conduction electrons. The direction of the current is defined as the opposite direction of the conduction electrons.

2.2 Electrolysis Certain chemical compounds conduct electricity when they are melted or dissolved in water. Solution containing salt and water is an electrolyte. In solution, sodium chloride will ionize giving + sodium ion Na and chloride ion Cl-: NaCl → Na + + Cl − and Cl − ions are mobile ions and can move if a voltage is applied to the solution by means of two electrodes: an electric current is formed by negatively charged chloride ions Cl − moving to + the positive electrode (anode), and positively charged sodium ions Na to the negative electrode Na

+

(cathode). The conducting liquid is called electrolyte and the process is called electrolysis. Ohm’s law reminds valid for electrolytic current. Electrical current in organisms is generally not carried by electrons. Instead it is carried by the mobile ions, such as Na+, Cl-, K+ of electrolytic solutions. Ohm’s law reminds valid for electrolytic current. The typical order of resistivity for body fluid is about 1 Ω ⋅ m . This is eight order of magnitudes of the resistivity of copper. When a small dc current is applied to the body by means of two electrodes, one cathode and another anode, the body tissue will carry on the current. This happens because tissue fluid is an electrolyte and it contains a high percentage of salt ions, such as Na+, Cl-, K+. This is the basic principle of galvanic treatment used in beauty therapy.

2.3 Electrical resistance The rate of charge flow, the current, depends on the voltage and the electrical resistance provided by the conductor. Their relationship is summarized by the Ohm’s law , V I = R It states that the current in a circuit is directly proportional to the voltage established across the circuit and is inversely proportional to the resistance of the circuit: The resistance is measured in volts per ampere, a unit called ohm ( Ω). Typical light bulb has a resistance of 100 ohms, an iron or toaster has a resistance of 15-20 ohms. Inside a circuit, current is regulated by a device called resistors. Rules for resistors: • Resistance varies with temperature. For metals it increases with temperature. • Resistance depends on the nature of substance • For a resistor of given shape, its resistance is directly proportional to length (which is also the direction of the current path) and is inversely proportional to the cross section area A: L R =ρ A R is the resistance in ohms, L length in m, A area in m2. ρ resistivity in ohm-m.

A

A high resistivity indicates that the material is a good insulator, while a low resistivity means that the material is a good conductor.

L

------------------------------------------------------------------------Material Resistivity (Ω ．m) Characteristic -----------------------------------------------------------------------Copper 1.7x10-8 Good conductor Germanium 0.6 Fair conductor Body fluids 2-0.2 Fair conductor 9~14 Glass 10 Good insulator Mica 1011-15 Good insulator ------------------------------------------------------------------------

2.4 Electric circuit The equivalent resistance R of a series combination of resistance R1, R2, R3 …is : R= R1+ R2+ R3 +… The equivalent resistance R of a parallel combination of resistance R1, R2, R3 …is :

1 1 1 1 = + + + ... R R1 R2 R3

2.5 Electric power A current moving in circuit converts its potential energy to other form of energies: thermal energy, mechanical energy, light energy…. It is proportional to electric potential difference ∆ V and charge q: i.e. ∆EPE = ∆V ⋅ q

The rate at which electric energy is converted into other form of energy is called electric power. i.e. ∆EPE ∆V ⋅ q P= = = ∆V ⋅ I t t ∆ V can be simplified to voltage V. Thus electric power P is equal to the product of current and voltage: P = IV Power has the unit of J/s, or watts (W), thus 1 A x 1V =1W. When current passes through a resistor R, the electric energy is converted to other energy and is related to the resistance by Ohm’s law: V2 P = I 2R = R

2.6 Direct current (dc) and alternating current (ac) When the charge flow is uni-directional, the current is called direct current (dc), If the direction of the charge flow changes from moment to moment, the current is referred to as alternating current (ac).

In a circuit, if the current is dc, both voltage and current are constant in time; if the current is ac, the voltage and current vary sinusoidally with time. V =V0 sin 2πft I = I 0 sin 2πft

The heights of the waves give peak current Io and peak voltage and Io=Vo/R. In HK, the frequency of the ac mains is 60 Hz, is, the current varies 60 cycles in 1 s.

2.7 Average power and peak power 2 The power of an ac current is P = IV = I oV sin 2πf and is time-varying. Its peak value is IoVo. So the average power

∴Pave =

1 peak power = 12 I 0V0 2

Similarly we define average current (rms or effective) and average voltage of an ac current:

I rms = From above:

I0

Vrms =

2

Pave = I rmsVrms =

I o Vo 2

2

=

1 I oVo 2

Unit 8 Electricity II 1. Electrical signal transmission through nerves 1.1 Bioelectric potentials

V0 2

Vo. that

Bioelectric potentials are involved in nerve impulses, brain conductivity, heartbeat, muscle contraction, etc. They are caused by ionic activity in excitable cells, such as nerves and muscles. Bioelectric potentials can also be called signals, or electric voltages.

1.2 Nerve cells The nervous system controls the movement of the body. The neuron, or nerve cell (神經細胞, 神 經元) is the basic component of nervous system. The nucleus of the nerve cell is located in the spinal cord. The part of the nerve cell which carries messages to the muscle is called the axon. The axon is a long fiber which is usually a few micrometers in diameter and a meter or longer in length. The axon is immersed in body fluid and is enclosed by a selectively permeable (semi-permeable) membrane. The body fluid is an electrolyte solution (like water), and contains sodium (Na+), potassium

salt

(K+), and chloride (Cl-) ions. These ions are located both inside and outside of the cell. When the cell is at rest, K+ and Cl- can pass through its membrane easily while sodium ions cannot.

1.3 Resting potential When the cell is at rest, the sodium potassium pump pumps sodium out of the cell, and potassium into the cell. This is an active process. Therefore there is a high concentration of sodium outside the cell and a high concentration of potassium inside the cell. However, the cell membrane is relatively impermeable to sodium, but quite permeable to potassium. Therefore, most of the sodium is kept outside the cell, but potassium can diffuse out of the cell. This is a passive process. This keeps the potential inside the cell negative compared to the outside of the cell. This cell voltage is called resting potential and is usually -70 mV to -90 mV. The cell is said to be polarized in its resting state.

1.4 Action potential

When a voltage is applied to the nerve cell membrane, or when other external stimuli are applied to the nerve cell, the membrane becomes permeable to sodium. Sodium rushes into the cell, and the electric potential of the cell becomes positive compared to its environment. The potential reaches about +20 mV. The cell is now depolarized. The membrane then becomes less permeable to Na+ ions and more permeable to K+ ions. Potassium diffuses out of the cell to restore the electric potential (repolarization). The diffusion of sodium and then potassium causes changes in the membrane potential. This is called an action potential. After the action potential is over, the sodium-potassium pump restores the sodium potassium gradient between inside and outside of the cell. The cell is now ready to respond to another stimulus.

2. The Electrocardiogram (ECG) The heart acts as double pump and consists of four chambers with valves. Blood from the body flows into the right atrium and then the right ventricle. Then, then blood is pumped to the lung. The oxygenated blood from the lung flows into the left atrium and then the left ventricle. Then it is pumped into the body. The heartbeat is synchronized and regulated by electrical impulses (stimuli). The heart beats as a single entity. The normal heartbeat rate is about 70 beats/min.

During each heartbeat, electrical stimuli spreads across the heart, causing potential differences between the polarized and depolarized cells. These potential differences appear collectively on the surface of skin as electric voltages that can be measured by electrodes suitably placed on the skin. They are displayed as specific bioelectric signal patterns, known as electrocardiogram abbreviated ECG. Shown in the figure is a typical ECG pattern recorded from the surface of the body. It is made up of three parts: • The P-wave: representing the depolarization of the atria, causing them to contract. • The QRS-complex: corresponding to the depolarization and contraction of the ventricles.

•

The T-wave: resulting from repolarization and relaxation of the ventricles.

The ECG is usually recorded on a chart or displayed on a cathode ray oscilloscope. The wave form measured at the body‘s surface depends not only on the individual person but also on the position of the electrodes. For a typical ECG pattern recorded on the surface of the body, peak amplitude values are as follows: P-wave: QRS-complex: T- wave:

0.2 mV 1 mV 0.1 to 0.5 mV

The shape of the signal at any one location will depend on the state of health of the heart muscles. Consequently the study of an ECG gives diagnostic information about the heart. Some common cardiac disorders that can be diagnosed with an ECG are: • High pulse rate (tachycardia) • Low pulse rate (bradycardia) • Ventricular fibrillation – irregular contraction of heart muscles • Damaged heart muscle – wave heights are reduced •

Heart blockage – part of the trace is missing

3. The defibrillator The heart is able to perform its important pumping function only through precisely synchronized action of the heart muscles. Under the action potentials the two auricles chambers contract and pump blood into two ventricles. After a delay time, the ventricles are synchronously activated to pump blood into body and lungs. If this synchronism is lost, it is called fibrillation. The condition of fibrillation is observed on an ECG as a very irregular trace. The fibrillation of ventricles can lead to death in a very short time. To stop defibrillation, two electrodes or paddles are placed on the skin one on each side of the heart. The potential difference across the electrodes is about 5000V and the energy stored in a 10.0 µ F capacitor of the defibrillator is order of 100J. The effect of the electric shock is to make all the heart muscles suffer a major contraction. This should then jolt the heart back to its normal rhythm.

4. The artificial pacemaker The pumping action of the heart is controlled by sino-atrial (SA) and atrio-ventricular (AV) nodes. For a resting adult, the heart has pulse rate of about 70 per minute. If the AV node become damaged, the heart does not stop but instead it goes into automatic control at a pulse rate of 30 per minute. This rate is sufficient to maintain life, but only if the person is very inactive. Artificial pacemakers can provide electrical pulses directly to the heart and replaces the action of the AV node. The pacemaker is inserted into the body and the wire is fed through a vein to appropriate position in the heart. The batteries powering the pacemaker last for several years. Early pacemaker produces pulses at a fixed rate of 70/min. Modern pacemakers can change their pulse rate, dependent on the oxygen demands of the body.

An artificial pacemaker, in-situ, shown by X-ray imaging.

5. Physiological effects of current Biological tissue contains free charge so that it is meaningful to consider it as an electrical conductor. Bound charges are also present in tissue so that dielectric properties also exist. These properties might arise as polarization of molecules in the tissue. The electrical conduction is the dominant factor when relatively low frequency (lower than 100 kHz) electric current is applied to the tissue. Electric current has three mains effects on the tissue; they are electrolysis, neural stimulation and heating. Neural stimulation is potentially the most dangerous effect, as the nervous system controls the two important systems: the circulation of blood and respiration. 5.1. Electrolysis Electrolysis will take place when a direct current (current with a frequency below 0.1 Hz) is passed through tissues which contain free ions. The positively charged ions will migrate to the negative electrode, and the negatively charged ions to the positive electrode. If two electrodes are placed on the skin, and a direct current of 100 µ A is passed beneath them for a few minutes, small ulcers will be formed beneath the electrodes. These ulcers take a very long time to heal. 10 µ A is the limit of safety for such dc current. 5.2. Neural stimulation At frequencies above 10 Hz, electrolysis appears to be reversible and the dominant effect is neural stimulation. The co-ordinated pumping activity of the heart can be disrupted by electric currents which pass through the heart. This is called fibrillation and can continue after the current is removed. Stimulation becomes increasingly difficult at frequencies above 1 kHz. There are two major ways of stimulation: indirect stimulation (stimulation through the skin), and direct stimulation (direct stimulation of the heart).

Indirect stimulation For main commercial supply frequencies (50-60 Hz), the threshold of the sensation is about 1 mA. A 5 mA current is the maximum harmless current above which sensory nerves are stimulated. At about 15 mA, the skeletal muscles will be stimulated to contract continuously, and it will not be possible to release an object held in the hands (can’t let go). As the current is further raised, it becomes increasingly painful, and difficult to breathe; at about 100 mA ventricular fibrillation begin. Currents up to 500 mA will cause ventricular fibrillation which will continue after the current stops flowing, and burns will be caused by the heating of the tissue. At currents above 500 mA the heart will restart spontaneously after the current is removed-this is the principle of the defibrillator.

Direct stimulation The direct passage of current through heart causes ventricular fibrillation even the amount of current is as small as 100µ A, which is much smaller than the threshold current by indirect stimulation. 5.3. Tissue heating At frequency above 10 kHz, electrical currents will not stimulate nerves but they will cause heating through I2R. Radio frequency energy (usually 27 MHz) is applied between two metal plates so that part of the energy is absorbed in the tissue, this is known as diathermy. High frequencies between 400 kHz and 30 MHz are used in surgical diathermia/electrosurgery to give either coagulation or cutting.

6. Electrical safety Electromedical equipment is a possible source of hazards to the patient. In many cases the patients directly connected to the equipment so that a fault current may flow through the patient. The skin can have a resistance as high as 1 M Ω for dry skin and falling to 1k Ω for wet skin. Internally the body resistance is about 50 Ω. For a person with wet skin touching both terminal of a 240 V voltage source, the current would gives rise to I=V/R=240/2050=117mA, which is enough to cause ventricular fibrillation. Hints for the electric equipment safety: • Never overload circuits. • Check for UL (Underwriter’s Laboratory) approval. • Ensure that appliances are grounded. • Study instructions on use of equipment. • Disconnect appliances when not in use. • Inspect all electrical equipment regularly. • Keep wires, plugs, and equipment in good repair. Use one plug per outlet. • Avoid contact with water or metal when using electricity. • Keep cords off floor to avoid tripping. • Do not leave room when patient is connected to any electrical device. • Do not attempt to clean around electrical outlets while equipment is plugged in. • Disconnect appliances by pulling plug, not cord. • Do not attempt to repair electrical appliances unless you are qualified. • Do not step on or set objects on electrical cords. Safety devices

Checklist Unit_8 • recall electric charge, electrostatic forces • recall the unit of charge and charge of electrons • Understand conductors and insulators • Recall the definition of electric potential difference • Recall capacitor: charge stored on a capacitor, energy stored on a capacitor, calculation of capacitance • Recall the definition of electric current • Application of Ohm’s law • Recall resistance and resistivity of resistors • Recall electric power and energy • Dc current and ac current, average power and peak power, effective (rms) and peak current or voltage • Recall resting/action potentials, related polarization /depolarization of a nerve cell • Describe the basic features of a typical ECG waveform • Know the basic electric safety precautions

Unit 9: Magnetism 9.1 Magnets Working principle of compass Magnets were used as navigational compasses. Since the Earth is like a giant magnet with a north and a south pole, the magnetic north pole of the compass is closely aligned with the geographic south pole of the Earth. Rules of magnetic force There are several rules for magnetic force:  There are only two magnetic poles: the north and south pole  Like poles repel, unlike poles attract  In magnetic substances, like iron, each atom is a small magnet 

 A larger magnetic force is produced when these tiny magnets are aligned in the same direction Therefore, for all practical purposes, a magnet can be divided indefinitely.

9.2 Magnetic field Since magnets attract small iron particles and a compass needle is affected by the Earth's poles, magnetic fields are associated with magnets. A magnetic field is stronger at the poles. The magnetic needle points in the same direction as the magnetic field lines.

Magnetic field created by a wire carrying current In addition to magnets, a magnetic field can also be generated by a wire carrying current. The direction of such a field is determined by the right hand rule.

9.3 Electromagnets

The strength of the magnetic field can be increased if the wire is coiled, or solenoid. The direction of such a field is also determined by the right hand rule. When an iron bar is put into the coil, the magnet becomes even stronger. This is a simple electromagnet. The strength of the electromagnet can be also enhanced by increasing the number of turns in the coil or the current intensity. The cause of magnetism The cause of magnetism has been proposed to be the electron spin or orbit.

(a) In the planetary model of the atom, the electron spins around the nucleus, creating a closed current loop, along with a magnetic field with north and south poles.

(b) Electron spin model: Electrons have spin, and can be roughly depicted as a rotating charge which creates a current along with a magnetic field with north and south poles. The theory of magnetism proposed by modern physics, is different from both the planetary model and the electron spin model. Circuit breaker

The circuit breaker is a typical application of the electromagnet. The electromagnet can create a strong magnetic field. The electromagnet of the circuit breaker is usually not strong enough to attract the iron bolt under the normal current range. However, if there is a fault which causes a current surge, the iron bolt is pulled out of the plunger by the electromagnet. Hence, the circuit is broken.

9.4 Dc motor Magnetic force on current-carrying wire Fleming’s left-hand

(motor) rule According to the Fleming’s left-hand (motor) rule, F is proportional to B, I and l.

(a) (b) (c) The magnetic field B (directed into the plane) exerts a force on the current-carrying wires. There are three cases of force exertion. (a) I=0, (b) I upward, (c) I downward. The magnetic force on the current carrying wire is the basis for the dc motor. The motor principle

The rectangular loop carrying a current I is in the presence of the uniform magnetic field B. The forces on the two horizontal sides "a" will cancel each other. However, the magnitude of force on the b sides is not zero. They are the same magnitude but opposite in direction. Hence, these two forces will produce a torque about O that will rotate the loop in a clockwise direction.

When the coil is vertical, the current should change its direction and then the coil will continue to turn. A split ring ensures that the current flow changes direction at the right time. This is the principle of the dc motor.

9.5 Hall effect Magnetic force creates a separation of charge which builds up until it is balanced by the electric force. An equilibrium is quickly reached. ε = Blv

Blood velocity Measurement The Hall effect can be applied in blood velocity measurement, assuming the blood is a conductorcarrying fluid. The velocity of the blood can be described by the following equation where ε is Hall emf. ε = Blv The electromagnetic and ultrasound techniques are two most used methods for the the measurement of the blood velocity: • The features of ultrasound technique are as follows: • In clinical application, it is most frequently utilized to detect the presence or location of blood flow rather than to measure its magnitude accurately • The frequency shift is in the audio range and is made audible with loudspeaker. • The popularity of the magnetic technique is the result of the following factors: • Utilized normally during surgical procedures in which blood vessels are exposed . • Producing accuracies up to 5% • Accommodation of blood vessels of diameters from 1mm to 20 mm

9.6 Electromagnetic induction The phenomenon of electromagnetic induction We have learnt that a current-carrying wire in a magnetic field will experience a force and that a current loop in a magnetic field will experience a torque. Now a torque in a magnetic field can create a current. The induction phenomenon deals with the creation of an electric current (or electro-motif force emf) in a loop by varying the magnetic fields (either in direction or magnitude). Experiments of electromagnetic induction First experiment:

A moving magnet can induce a current in a loop even if there is no battery in the loop. Second experiment:

The current meter registers a current in the left hand loop at the moment the switch S is opened or closed. No motion of the coils is involved.

Third experiment:

A current is induced when the rod moves to the right in a uniform constant magnetic field.

Laws of electromagnetic induction Faraday’s law of induction is one of two important laws of electromagnetic induction. A potential difference can be induced in a loop if there is a change in the strength of magnetic field, loop area, or angle between the magnetic field and the loop. Faraday’s law of induction:

ε =−

∆( BA cos θ ) ∆t

Another important law is Lenz's law. It states: An induced current has a direction such that it induces a magnetic field which opposes the changes in the magnetic flux.

9.7 AC generator The Generation of Alternative Current

ε = −BA

∆ (cos θ ) = BA ω sin θ ∆t

Faraday’s law is the basis of ac current generation. In order to generate an ac current, it is not necessary to move the magnet. Instead, one can rotate the coil of wire between the poles of the magnet. The induced potential difference (or current) is increased, if  the coil rotates faster,  the area of the coil is increased,  there are more turns on the coil,  the strength of the magnet is increased. Simple ac generator

The generator has a fixed magnet and a rotating coil. The coil is connected to a conducting ring. Two conducting rings rotate together with the coil. The rings come into contact with two fixed carbon brushes. As the coil turns, the induced voltage changes direction for each half turn of the coil, this creates an alternating current.

9.8 Transformer Energy Transmission

For a household circuit, electricity produced in power stations is first stepped up to a high voltage (> 10 kV) by a step-up transformer, and then delivered to a local area through high tension cable towers. A stepdown transformer is later used to step down the voltage to a domestic level (rms 220 V in Hong Kong). For safety reasons, low voltages are required at both the generating and receiving end in energy transmission. Besides, the energy loss in the transmission line is I2R and the power output is IV. Hence, we have to raise V during transmission in order to minimize I and thereby reduce the power loss in the transmission line. The device with which we can raise and lower the voltage is called the transformer. The Transformer Principle

A current in the 2nd coil is generated only when the 1st coil is turned on or off. A changing magnetic field in a fixed coil will induce a current in a second fixed coil. The iron core provides a magnetic link between the two coils.

Transformers

Transformers use a magnetic link between two coils to step-up or step-down alternating voltage. Transformers work with alternating current only. The primary coil must use an alternating current to produce a changing magnetic field in the iron core; an alternating current is induced in the secondary coil. There are two types of transformation: voltage and current. Voltage transformation formula:

where V1 and V2 are the primary and secondary voltages, and N1 and N2 are the number of turns on the primary and secondary coils Current transformation formula:

where I1 and I2 are the primary and secondary currents, and N1 and N2 are the number of turns on the primary and secondary coils Example: A transformer is designed to step-down from 230 V to 11.5 V. There are 1000 turns of wire on the primary coil. Calculate: 1) the number of turns on the secondary coil 2) the output current for an input current of 0.01 A 1) V1 V = 2 N1 N 2

230 11 .5 ∴ = 1000 N2

N2= 50 Turns 2)

I1 N1 = I 2 N 2 ∴0.01 ⋅1000 = I 2 ⋅ 50

I2=0.2 A