Unit 7 Presentation

Unit VII: Electricity Electrostatics  Electric voltage  Capacitors  Electric current  Electrolysis Electrical resistance Electric power

An ECG machine

A defibrillator

What is electrostatics When a glass rod rubbed with silk •the glass rod becomes positively charged, •the silk becomes negatively charged.

(a)The glass rod is attracted to the silk. (b) Two similarly charged glass rods repel. (c)Two similarly charged silk cloths repel.

The effects of electrostatics are explained by a physical called electric charge. There are only two types of charge, one called positive, other negative. The rules for electric charge:

•Same charges repel, •opposite charges attract

How to quantify the charge The electric charge q is : • a physical property of atom • has the unit Coulomb in SI unit, abbreviated C 1 C = 6.25 x 1018 electrons • the charge of an electron = that of proton, but opposite in sign: qe = 1.60 ×10 −19 C

Electrostatic force The attraction or repulsion forces between charges are called electrostatic force, the electrostatic force: •decreases with distance •increases with quantity of charges 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. r

q1

r

q2

(a) Opposite charges

q1

q2

(b) like charges

Charging by contact Electrons can be transferred from one object to another by simple touching: charging by contact

Metal knob Metal stem Gold leaves

An electroscope

Charging by induction (a)Two metal spheres in contact but isolated (b) A positively charged glass rod is brought near (c)The spheres are separated (d)Removing the rod, the spheres retain net charges

Charge polarization Charging by induction in insulators takes place differently: •no free charge flows • the center of positive charge and negative charge shift slightly: charge polarization.

Application: Lightening rods Charging by induction : •causing lightening strike •Negatively charged clouds induce positive charges on the building Lightening rods: •Collect electrons in air •prevent the buildup of large excess “+” charges on the buildings

Xerography

Laser Printers

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 from 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 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.

+

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

∆EPE = ∆V ⋅ q The unit of electric potential is volts (V), 1 Volt (V)=1 Joule (J)/1 Coulomb (C).

Capacitors What is a capacitor? A capacitor is a device that can store electric potential energy and consists of two oppositely charged conductor plates that are separated by a distance d. +Q

-Q E d

Charging a capacitor

Discharging a capacitor

Capacitance The capacitance C is defined as : +Q

-Q E

Area A

Q C= ∆V

d

• q is the magnitude of charge stored on each plate • ∆ V is the voltage applied •The SI unit of capacitance is farad (F): 1 F= 1 C / V •The electric potential energy stored in a capacitor:

1 2 U = C ⋅ ∆V 2

Parallel plate capacitor +Q

-Q E

Area A

κ εo A C= d

d

∀ε o =8.85 x 1012 • κ is the dielectric constant of the dielectric material

capacitors

Example: A heart defibrillator delivers 400J of energy by discharging a capacitor initially at 10000V. (a) What is its capacitance? (b) What is the charge stored in the capacitor?

(a) Energy stored in a capacitor:

2U 2 ⋅ 400 1 −6 2 = 8 ⋅10 F U = C ⋅V ∴ C = 2 = 2 V 10000 2 (b) Charge stored in the capacitor: −6

−2

Q = CV = 8 ⋅10 ⋅10 = 8 ⋅10 C 4

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=10-9 m). Membranes act as dielectric of a 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 gives a value of κ≅ 10 for the membrane. Knowing C κ εo that = A

d

Electric current

•The flow of electric charges in a conductor •caused uniquely by the electric potential difference (or voltage) •An electric power source is provided to maintain the voltage •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. •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.

Electric current the current I is given by :

∆q I = ∆t ∆ q :the amount of the charge crossing a surface  ∆ t, the time needed, The SI unit of current is ampere (A), 1 A= 1 C/s In metals, the charges are provided by free electrons, or

conduction electrons. The direction of the current is defined as the opposite direction of the conduction electrons.

Electrical resistance Ohm’s law :

V I= R

the current in a circuit is directly proportional to the voltage And inversely proportional to the resistance of the circuit  The resistance is measured in volts per ampere, a unit

called ohm (Ω )

A

L: length in m, A: area in m2 R: is the resistance in ohms, ρ : resistivity in ohm-m,

L

A high resistivity indicates that the material is a good insulator, while a low resistivity means that the material is a good conductor. -------------------------------------------------------------------------Material Resistivity (Ω •m) Characteristic -------------------------------------------------------------------------Copper 1.7x10-8 Good conductor Germanium ~0.6 Fair conductor Body fluids 2-0.2 Fair conductor Glass 109-14 Good insulator Mica 1011-15 Good insulator --------------------------------------------------------------------------

Resistance in series and parallel •In series

Rs = R1 + R2 + R3 + R4 •In parallel 1 1 1 1 = + + + ⋅⋅⋅ R p R1 R2 R3

Example: Current and voltage in a circuit A 1.5 V battery with an internal resistance of 5 Ω is connected to a light bulb with a resistance of 20 Ω in a sample, single-loop circuit. a. b.

What is the current flowing in this circuit? What is the voltage difference across the light bulb?

Solution: •

V = 1.5 (V), Rbattery = 5 Ω, Rbulb = 20 Ω, find I The total resistance of the circuit is

R = Rbattery + Rbulb = 25 Ω

By Ohm’s law, I = V/R = 1.5 V / 25 Ω = 0.06 A (or 60 mA) b.

To find Vbulb ,

Vbulb = IR = (0.06 A) ( 20 Ω) = 1.2 V

Note: As a battery gets older, its internal resistance gets larger and larger. The total resistance of the circuit increases and reduces the current flowing through the circuit. As the current gets smaller and the bulb becomes dimmer until finally its glows no more.

Electric power •How energy transformation take place in a circuit? In a water-flow system or an electric circuit, the energy transformation looks like: energy source → potential energy → kinetic energy →other energy

∆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

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: 2

V P=I R= R 2

Example: The power dissipated in a 20 Ω light bulb powered by two 1.5 V batteries in series is: V = V1 + V2 = 1.5 + 1.5 = 3 V; R = 20 Ω By Ohm’s law, I = V/R = 3 V / 20 Ω = 0.15 A Therefore Power dissipated, P = I2R = (0.15)2 (20 Ω ) =0.45 W This can be checked by calculating the power delivered by the batteries: P = VI = (3V)(0.15A) = 0.45 W

Direct current (dc), alternating current (ac) In a circuit, a voltage applied to a resistor R:

I = I 0 sin 2πft

V = V0 sin 2πft

•dc current : charge flow is uni-directional, •ac current : the direction of the charge flow changes from moment to moment, Vo Vo: peak voltage Io: peak current I o =

R

Average power and peak power The power of an ac current is and is time-varying. Its peak value is IoVo. So the average power Pave ∴ Pave

1 = peak power = 12 I 0V0 2

Irms : average current Vrms : average voltage Vrms

V0 = 2

I rms

∴ Pave = I rmsVrms

I0 = 2

Irms : effective or rms current Vrms : effective or rms voltage I o Vo 1 = = Vo I o 2 2 2