Current Electricity

Current electricity – chap 21,22,23

Electric Charge

• Electric current = a flow of electric charges. The electrons, which orbit the nucleus at relatively large distances can sometimes become free to move → electric current. • Electric charge is measured in coulombs (C) • The charge on an electron = e = 1.6 x10-19C

Conductors and insulators • Conductor – substance which allows electric current to flow through it • Insulator – substance which does not allow electric current to flow through it

Current

Electric current (I)= amount of charge passing a point every second. Measured in Amperes (A). Measured using an ammeter, or for very small currents, a galvanometer Current = Charge / time I=Q/t

Conventional Current.

• Current = movement of electrons • Electrons move from negative to positive • However traditionally current was thought of as flowing from positive terminal of a battery to the negative (wrong way round) • We still use this convention todaycurrent is thought of as flowing from positive to negative (conventional current)

DC and AC

• Two types of current exist • Direct current-always flows in the same direction – this is the type of current you get from a battery • Alternating current – here the current reverses direction many times per second-this is the type of current you get from the mains

Potential difference

• Water flows in a pipe if there is a height difference between the two ends-similarly current flows in a conductor if there is a potential difference between the two ends. • The potential difference between two points is defined as the energy lost by one coulomb as it moves from one point to the othermeasured in volts. • 1Volt = 1joule per coulomb

Definition of potential difference • Since work = energy we can also define potential difference as • Potential difference = work done in bringing a unit charge from one point to the other •

V=W/Q

Electrical power • • • But Q/t = I

W=VQ W / t = V Q/t

• Thus W/t = VI • W/t = rate of doing work which is called the power • P = VI

Electromotive force (emf) • EMF = the voltage between two ends of a circuit when no current is flowing in the circuit

Sources of EMF

1. Electric cells-convert chemical energy to electrical energy Consists of 2 different metals (the electrodes) immersed in a substance called an electrolyte. A battery consists of a no. of cells connected together (a car battery = 6 2V cells in series) Primary cell

Battery of cells

Simple Cell

• Cu plate and Zn Plate in a beaker of dilute sulphuric acid

Cu

Zn Dilute sulphuric acid

The plates react with the acid – Zn plate becomes neg. charged, Cu +. Thus a potential difference exists so electrons can flow from neg to + plate

Primary and Secondary cells

• Primary cell = cell which cannot be recharged-once the chemicals are used up it must be discarded (e.g. dry battery) • Secondary cell = cell which can be recharged (usually by pushing current through it in the wrong direction) (e.g. car battery)

Ohm’s Law

• For a metallic conductor at constant temperature, the current flowing through the conductor is directly proportional to the p.d. across the conductor • V = constant I • The constant = resistance • V=IR

Resistance • Electric currents (electrons) flow through conductors. • As they do so they collide with atoms in the conductor and so lose energy. • The material of the conductor RESISTS the current

• If a conductor has a large resistance, then a large p.d. will only give a small current • If a conductor has a small resistance, then a large p.d. will give a large current • R=V/I • Resistance is measured in Ohms. • A conductor has resistance 1 Ω if the current through it is 1 amp when the p.d. = 1V

To measure resistance • Two ways 1. using an ohmmeter 2. by measuring current and voltage and using the formula that V=IR

Experiment • To demonstrate Ohm’s Law P258

Resistors • Devices specially made to have a certain value of resistance • Can be either fixed or variable • Variable resistor-either a rheostat or a potentiometer – by moving the sliding contact you vary how much of the wire the current must pass through (i.e. the resistance)

Connecting Circuits • 2 ways to connect • Series

• Parallel

R1

R2

R1 R2 R3

R3

Series Circuit • Current has only one path → Itotal = I1 =I2 =I3 Voltages add Vtotal = V1 +V2 +V3 From Ohm’s law V = I R→ Itotal Rtotal= I1R1 +I2R2 +I3R3→ Rtotal= R1 +R2 +R3

Parallel Circuit

• Current has several paths → Itotal = I1 +I2 +I3 Voltages stay the same Vtotal = V1 =V2 =V3 From Ohm’s law V = I R→ Vtotal /Rtotal= V1/R1 +V2/R2 +V3/R3→ 1/ Rtotal= 1/R1 +1/R2 +1/R3 • Do questions p260

Kirchoff’s Laws • The sum of the currents entering a junction = sum of the currents leaving the junction • The emf across the circuit = sum of the emfs across the individual parts of the circuit

Measuring current and voltage • Currents are measured using an AMMETER which is placed in SERIES • Voltages are measured using a VOLTMETER which is placed in PARALLEL

Factors effecting resistance • Resistance of a conductor depends on • Length of conductor (l) • Temperature of the conductor • The cross sectional area of the conductor • The material from which the conductor is made

Effect of temperature on resistance of a metal • The resistance of a metal increases with increasing temp. • As the temperature of the metal increases the atoms of the metal vibrate more. This means that as the electrons try to pass through (electric current) they collide more and so lose energy →resistance increases

Resistance Ω

Ctd.

Temp T/oC

• For moderate changes in temp. the change in resistance is proportional to the change in temp. – graph does not pass through the origin thus the resistance changes linearly with temperature (NOT directly proportional)

Effect of temperature on resistance of semiconductors or insulators • In an insulator (or cold semiconductor) there are no electrons free to move and so no current. • As you heat the semiconductor some electrons break free of their bonds and so become free for conduction→the resistance decreases

Thermistor

Resistance Ω

• This is a semiconductor whose resistance decreases rapidly with increasing temp. • NOTE the relationship is not linear

Temp. T

Experiment • To investigate the resistance of a metallic conductor with temp. P263 • To investigate the resistance of a thermistor with temperature P264

Other factors affecting resistance • At constant temperature the resistance of a conductor depends on • Length • Cross-sectional area • The material from which the conductor is made

• Experimentally it can be shown • R∝l •

R ∝ 1/A

• Thus R∝l/A • Thus R = constant l / A • This constant is called the resistivity (ρ) and depends on the material of the conductor • Thus R=ρl/A

• often, we are measuring the resistance of wires. In these cases the cross sectional area is the area of a circle A = πr2 where r = radius • Thus R = ρ l / πr2 • Or, since r = d/2 (where d = diameter) R = ρ 4l / πd2

Resistivity (ρ) • Defined as the resistance per unit length per unit cross sectional area • ρ = RA / l • Do questions p269

Experiment

• To measure the resistivity of the material of a wire • Use a micrometer screw gague to measure the diameter of the wire at several places, then take an average • Measure R using ohmmeter, or by measuring current and voltage

Wheatstone bridge • A device for measuring the value of an unknown resistance • The values of the resistances are varied until no current flows through the galvanometer

R1

B R2

A

C R3

R4 D

• At this point, the potential at B =potential at D (since no current flows) • Thus p.d. between A and B = p.d. between A and D (VAB=VAD) • Similarly VBC = VDC • From Ohm’s law V = IR • •

I1R1 = I2R3 I1R2 = I2R4

• Thus R1 / R2 = R3 / R4 • • Thus, if three of the resistors are known, you can calculate the value of the last. • Experimentally a resistor is placed in series with the galvanometer to protect it from too much current. This resistor is then removed when the aprox. balance point is found

Metre bridge • This uses the same logic as the wheatstone bridge, but two of the resistors are replaced by a length of wire. A sliding contact divides the wire into two lengths, and so into 2 resistances. This makes it easier to adjust the resistance

R2

R1 G

L1

Length of wire

• The position of the sliding contact varies L1 and L2

L2

• We know from the wheatstone bridge circuit R1 / R2 = R3 / R4 • In this case R3 and R4 are wires of uniform cross section (A) and the same material (ρ is the same) • Thus R3 =constant L1 R4 = constant L2 • •

R1 / R2 =L1 / L2

Uses of wheatstone bridge circuits • Temperature control – in this case the wheatstone bridge starts balanced. If the temperature of one of the resistors changes then its resistance will change, the bridge will no longer be balanced and so current flows through the galvanometer.

• The size and direction of the current indicate the size and direction of the temperature change, and so can be used to control a heater and bring the temp. back to its original value

• Fail-safe device – if the pilot light in a gas boiler goes out, you need the gas to shut off automatically. • A thermistor placed near the flame is used as one resistor in a wheatstone bridge. If the flame goes out the resistance increases, unbalances the bridge and current flows in the galvanometer. This current can be used to cut off the fuel

Potential divider circuit • If two or more resistors are connected in series the total potential difference is divided between the resistors. • The bigger the resistor the bigger the potential across it (if one resistor is much bigger than the other effectively all the p.d. is across the big resistor)

Ctd. • Such a system of resistors is known as a potential divider circuit-used when a smaller p.d. is required than the supply

R1 R2

Vout

The value of Vout depends on R1 and R2

Variable potential divider circuit • Two resistors replaced by a variable resistor. The output voltage increases from O V when the contact is at A to the max input voltage when the contact is at B A

B

Vout