Electricity and Electricity and MagnetismMagnetism

Topic Topic 55..22 Electric CircuitsElectric Circuits

Electromotive ForceElectromotive Force Defining potential differenceDefining potential difference The coulombs entering a lamp have electrical The coulombs entering a lamp have electrical

potential energy;potential energy; those leaving have very little potential energy.those leaving have very little potential energy. There is a There is a potential difference potential difference (or p.d.) (or p.d.) across across

the lamp, because the potential energy of each the lamp, because the potential energy of each coulomb has been transferred to heat and light coulomb has been transferred to heat and light within the lamp.within the lamp.

p.d. is measured in p.d. is measured in volts volts (V) and is often called (V) and is often called voltage.voltage.

The The p.d. p.d. between two points is the between two points is the electrical potential energy transferred to electrical potential energy transferred to other forms, per coulomb of charge that other forms, per coulomb of charge that passes between the two points.passes between the two points.

Resistors and bulbs transfer electrical Resistors and bulbs transfer electrical energy to other forms, but which energy to other forms, but which components provide electrical energy?components provide electrical energy?

A dry cell, a dynamo and a solar cell A dry cell, a dynamo and a solar cell are some examples.are some examples.

Any component that supplies electrical Any component that supplies electrical energy is a source of energy is a source of electromotive electromotive force or e.m.f. force or e.m.f.

It is measured in volts. It is measured in volts. The e.m.f. of a dry cell is 1.5 V, that of a The e.m.f. of a dry cell is 1.5 V, that of a

car battery is 12 Vcar battery is 12 V

A battery transfers chemical energy to electrical A battery transfers chemical energy to electrical energy, so that as each coulomb moves through energy, so that as each coulomb moves through the battery it gains electrical potential energy.the battery it gains electrical potential energy.

The greater the e.m.f. of a source, the more The greater the e.m.f. of a source, the more energy is transferred per coulomb. In fact:energy is transferred per coulomb. In fact:

The e.m.f of a source is the electrical potential The e.m.f of a source is the electrical potential energy transferred from other forms, per energy transferred from other forms, per coulomb of charge that passes through the coulomb of charge that passes through the source.source.

Compare this definition with the definition of p.d. Compare this definition with the definition of p.d. and make sure you know the difference between and make sure you know the difference between them.them.

Internal ResistanceInternal Resistance

The cell gives 1.5 joules of electrical The cell gives 1.5 joules of electrical energy to each coulomb that passes energy to each coulomb that passes through it,through it,

but the electrical energy transferred in the but the electrical energy transferred in the resistor is less than 1.5 joules per coulomb resistor is less than 1.5 joules per coulomb and can vary.and can vary.

The circuit seems to be losing energy ‑ The circuit seems to be losing energy ‑ can you think where?can you think where?

The cell itself has some resistance, its The cell itself has some resistance, its internal internal resistance.resistance.

Each coulomb gains energy as it travels through Each coulomb gains energy as it travels through the cell, but some of this energy is wasted or the cell, but some of this energy is wasted or `lost' as the coulombs move against the `lost' as the coulombs move against the resistance of the cell itself.resistance of the cell itself.

So, the energy delivered by each coulomb to the So, the energy delivered by each coulomb to the circuit is less than the energy supplied to each circuit is less than the energy supplied to each coulomb by the cell.coulomb by the cell.

Very often the internal resistance is small Very often the internal resistance is small and can be ignored. and can be ignored.

Dry cells, however, have a significant Dry cells, however, have a significant internal resistance.internal resistance.

This is why a battery can become hot This is why a battery can become hot when supplying electric current.when supplying electric current.

The wasted energy is dissipated as heat.The wasted energy is dissipated as heat.

Resistance CombinationsResistance Combinations

Resistors in seriesResistors in series

The diagram shows three resistors connected in The diagram shows three resistors connected in seriesseries

There are 3 facts that you should know for a There are 3 facts that you should know for a series circuit:series circuit: the current through each resistor in series is the samethe current through each resistor in series is the same the total p.d., V across the resistors is the sum of the the total p.d., V across the resistors is the sum of the

p.d.s across the separate resistors, so: V = Vp.d.s across the separate resistors, so: V = Vll + V + V22 + +

VV33

the combined resistance R in the circuit is the sum of the combined resistance R in the circuit is the sum of the separate resistorsthe separate resistors

R = RR = Rll + R + R2 2 + R+ R33

Suppose we replace the 3 resistors with Suppose we replace the 3 resistors with one resistor R that will take the same one resistor R that will take the same current I when the same p.d. V is placed current I when the same p.d. V is placed across itacross it

This is shown in the diagram. Let's calculate R.This is shown in the diagram. Let's calculate R. We know that for the resistors in series:We know that for the resistors in series:

V = VV = Vll + V + V22 + V + V33

But for any resistor: p.d. = current x resistance But for any resistor: p.d. = current x resistance (V = I R).(V = I R).

If we apply this to each of our resistors, and If we apply this to each of our resistors, and remember that the current through each remember that the current through each resistor is the same and equal to I, we get:resistor is the same and equal to I, we get:

IR = IRIR = IRll+IR+IR22+IR+IR33

If we now divide each term in the equation by I, If we now divide each term in the equation by I, we get:we get:

R = RR = R11 + R + R2 2 + R+ R33

Resistors in parallelResistors in parallel

We now have three resistors connected in We now have three resistors connected in parallel:parallel:

There are 3 facts that you should know for a There are 3 facts that you should know for a parallel circuit:parallel circuit: the p.d. across each resistor in parallel is the samethe p.d. across each resistor in parallel is the same the current in the main circuit is the sum of the the current in the main circuit is the sum of the

currents in each of the parallel branches, so:currents in each of the parallel branches, so: I I = I= I11 + + II22 + + II33

the combined resistance the combined resistance R R is calculated from the is calculated from the equation:equation:

Suppose we replace the 3 resistors with Suppose we replace the 3 resistors with one resistor one resistor R R that takes the same total that takes the same total current I when the same p.d. V is placed current I when the same p.d. V is placed across it.across it.

This is shown in the diagram. Now let's calculate This is shown in the diagram. Now let's calculate R.R. We know that for the resistors in parallel:We know that for the resistors in parallel: I = II = I11+I+I22+I+I33

But for any resistor, current = p.d. = resistance But for any resistor, current = p.d. = resistance (I = V/R ).(I = V/R ). If we apply this to each of our resistors, and remember If we apply this to each of our resistors, and remember

that thethat the p.d. across each resistor is the same and equal to V, p.d. across each resistor is the same and equal to V, we get:V/we get:V/R=V/RR=V/R11 + V/R + V/R22 + V/R + V/R33

Now we divide each term by V, to get:Now we divide each term by V, to get: 1/1/R=1/RR=1/R11 + 1/R + 1/R22 + 1/R + 1/R33

You will find that the total resistance You will find that the total resistance R is R is always less than the smallest resistance in always less than the smallest resistance in the parallel combination.the parallel combination.

Circuit DiagramsCircuit Diagrams

You need to be able to recognize and use You need to be able to recognize and use the accepted circuit symbols included in the accepted circuit symbols included in the Physics Data Bookletthe Physics Data Booklet

Ammeters and VoltmetersAmmeters and Voltmeters

In order to measure the current, an ammeter is In order to measure the current, an ammeter is placed placed in series, in series, in in the circuit.the circuit.

What effect might this have on the size of the What effect might this have on the size of the current?current?

The The ideal ideal ammeter has zero resistance, so that ammeter has zero resistance, so that placing it in the circuit does not make the current placing it in the circuit does not make the current smaller.smaller.

Real ammeters do have very small resistances ‑ Real ammeters do have very small resistances ‑ around 0.01 around 0.01 ΩΩ..

A voltmeter is connected A voltmeter is connected in parallel in parallel with a with a component, in order to measure the p.d. across component, in order to measure the p.d. across it.it.

Why can this increase the current in the circuit?Why can this increase the current in the circuit? Since the voltmeter is in parallel with the Since the voltmeter is in parallel with the

component, their component, their combined combined resistance is less resistance is less than the component's resistance.than the component's resistance.

The The ideal ideal voltmeter has infinite resistance and voltmeter has infinite resistance and takes no current.takes no current.

Digital voltmeters have very high resistances, Digital voltmeters have very high resistances, around 10 Maround 10 MΩΩ, and so they have little effect on , and so they have little effect on the circuit they are placed in.the circuit they are placed in.

Potential dividersPotential dividers

A potential divider is a device or a circuit A potential divider is a device or a circuit that uses two (or more) resistors or a that uses two (or more) resistors or a variable resistor (potentiometer) to provide variable resistor (potentiometer) to provide a fraction of the available voltage (p.d.) a fraction of the available voltage (p.d.) from the supply.from the supply.

The p.d. from the supply is divided across The p.d. from the supply is divided across the resistors in direct proportion to their the resistors in direct proportion to their individual resistances.individual resistances.

Take the fixed resistance circuit - this is a Take the fixed resistance circuit - this is a series series circuit therefore the current in the circuit therefore the current in the same at all points.same at all points.

IIsupplysupply = I = I11 = I = I22

Where IWhere I11 = current through R = current through R11

II22 = current through R = current through R22

Using Ohm’s LawUsing Ohm’s Law

ExampleExample

With sensorsWith sensors

A thermistor is a device which will usually A thermistor is a device which will usually decrease in resistance with increasing decrease in resistance with increasing temperature.temperature.

A light dependent resistor, LDR, will A light dependent resistor, LDR, will decrease in resistance with increasing decrease in resistance with increasing light intensity. (light intensity. (LLight ight DDecreases its ecreases its RResistance).esistance).

ExampleExample

Calculate the readings on the meters Calculate the readings on the meters shown below when the thermistor has a shown below when the thermistor has a resistance ofresistance of

a) 1 ka) 1 kW (W (warm conditions) and b) 16 kwarm conditions) and b) 16 kW. W. ((cold conditionscold conditions))