physics support materials higher electricity and electronics b electric fields and resistors in...

Physics Support MaterialsPhysics Support MaterialsHigher Higher Electricity and ElectronicsElectricity and Electronics

Electric Fields and Resistors in CircuitsElectric Fields and Resistors in Circuits

3, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,

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An electron volt is a unit of energy. It represents the change in potential energy An electron volt is a unit of energy. It represents the change in potential energy of an electron which moves through a potential difference of 1 volt. If the charge of an electron which moves through a potential difference of 1 volt. If the charge on an electron is 1.6 x 10 on an electron is 1.6 x 10 -19-19 C, what is the equivalent energy in joules? C, what is the equivalent energy in joules?

3

Electric Fields and Resistors in Circuits

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Mass of an electron = 9.1 Mass of an electron = 9.1 xx10 10 -31-31 kg. Charge on an electron = 1.6 x kg. Charge on an electron = 1.6 x10 10 -19-19 C. The C. The electron shown below is accelerated across a p.d. of 500 V. (a) How much electron shown below is accelerated across a p.d. of 500 V. (a) How much electrical work is done?electrical work is done?



4

(b) How much kinetic energy has it gained?(b) How much kinetic energy has it gained?

(c) What is its final speed?(c) What is its final speed?

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Electrons are ‘fired’ from an electron gun at a screen. The p.d. across the gun is 2000 V. Electrons are ‘fired’ from an electron gun at a screen. The p.d. across the gun is 2000 V. After leaving the positive plate the electrons travel at a constant speed to the screen. After leaving the positive plate the electrons travel at a constant speed to the screen. Assuming the apparatus is in a vacuum, at what speed will the electrons hit the screen?Assuming the apparatus is in a vacuum, at what speed will the electrons hit the screen?



5

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What would be the increase in speed of an electron What would be the increase in speed of an electron accelerated from rest by a p.d. of 400 V?accelerated from rest by a p.d. of 400 V?



6

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400106.117

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101.9104.62

v

1-7 s m 102.1 v


An X-ray tube is operated at 25 kV and draws a current of 3 mA. An X-ray tube is operated at 25 kV and draws a current of 3 mA. (a) Calculate (a) Calculate (i) the kinetic energy of each electron as it hits the target (i) the kinetic energy of each electron as it hits the target



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(b) What happens to the kinetic energy of (b) What happens to the kinetic energy of the electrons?the electrons?

(ii) the velocity of impact of the electron as it hits the target(ii) the velocity of impact of the electron as it hits the target

(iii) the number of electrons hitting the target (iii) the number of electrons hitting the target each second.each second.

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It is transferred to the EIt is transferred to the Ekk of the X ray photon of the X ray photon


In the circuit opposite: In the circuit opposite: (a) what is the total resistance of the circuit(a) what is the total resistance of the circuit



11

(b) what is the resistance between (b) what is the resistance between X and YX and Y

(c) find the readings on the (c) find the readings on the ammetersammeters

(d) calculate the p.d. between X (d) calculate the p.d. between X and Yand Y

(e) what power is supplied by the (e) what power is supplied by the battery?battery?

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1 1 1R R RP

124

41

121 1

P R 3

412

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3

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612I )(AA 2 1I The current splits in the ratio of 12 : 4 or 3 : 1The current splits in the ratio of 12 : 4 or 3 : 1

The current through the 4 The current through the 4 resistor is 3/4 of 2 A or 1.5 A resistor is 3/4 of 2 A or 1.5 A

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The circuit opposite uses the 230 V alternating mains The circuit opposite uses the 230 V alternating mains supply. Find the current flowing in each resistor when: supply. Find the current flowing in each resistor when: (a) switch S is open (a) switch S is open

(b) switch S is closed. (b) switch S is closed.



12

2 1R R RS 20 S R

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An electric cooker has two settings, high and low. It takes 1 An electric cooker has two settings, high and low. It takes 1 A at the low setting and 3 A at the high setting.A at the low setting and 3 A at the high setting.



13

(a) Find the resistance of R(a) Find the resistance of R11 and Rand R22

(b) What is the power consumption at (b) What is the power consumption at each setting?each setting?

At the low setting, the switch is openAt the low setting, the switch is open 230

1230

1IV R

7. 763

230IV RP

At the high setting, the switch is closedAt the high setting, the switch is closed

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7. 761 1

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2230

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2230

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OpenOpen VIP

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(a) Find the value of the series resistor which would allow (a) Find the value of the series resistor which would allow the bulb to operate at its normal rating.the bulb to operate at its normal rating.



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(b) Calculate the power dissipated in (b) Calculate the power dissipated in the resistorthe resistor

VIP VPI A 3

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Finding the current through the bulbFinding the current through the bulb

The current through the bulb is the same as the current through the resistorThe current through the bulb is the same as the current through the resistor

IVR 4

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VIP W36312 P


In the circuit below, r represents the internal resistance of the cell and R represents In the circuit below, r represents the internal resistance of the cell and R represents the external resistance of the circuit. When S is open, the voltmeter reads 2.0 V. the external resistance of the circuit. When S is open, the voltmeter reads 2.0 V. When S is closed, it reads 1.6 V and the ammeter reads 0.8 A.When S is closed, it reads 1.6 V and the ammeter reads 0.8 A.



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(a) What is the e.m.f. of the (a) What is the e.m.f. of the cell?cell? (b) What is the terminal potential difference when S (b) What is the terminal potential difference when S is closed?is closed?

(c) Calculate the values of r (c) Calculate the values of r and R.and R.

(d) If R was halved in value, calculate the new readings on (d) If R was halved in value, calculate the new readings on the ammeter and voltmeter. the ammeter and voltmeter.

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The cell in the diagram has an e.m.f. of 5 V. The current through the lamp is The cell in the diagram has an e.m.f. of 5 V. The current through the lamp is 0.2 A and the voltmeter reads 3 V. Calculate the internal resistance of the cell.0.2 A and the voltmeter reads 3 V. Calculate the internal resistance of the cell.



16

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A cell of e.m.f. 4 V is connected to a load resistor of 15 A cell of e.m.f. 4 V is connected to a load resistor of 15 . If 0.2 A flows . If 0.2 A flows round the circuit, what must be the internal resistance of the circuit?round the circuit, what must be the internal resistance of the circuit?



17

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A signal generator has an e.m.f. of 8 V and internal resistance of 4A signal generator has an e.m.f. of 8 V and internal resistance of 4 A load A load resistor is connected to its terminals and draws a current of 0.5 A. Calculate the resistor is connected to its terminals and draws a current of 0.5 A. Calculate the load resistance.load resistance.



18

IrIRE

45.05.08 R

125.028R


(a) What will be the terminal p.d. across the cell in the (a) What will be the terminal p.d. across the cell in the circuit below.circuit below.



19

(b) Will the current increase or decrease as R is increased?(b) Will the current increase or decrease as R is increased?

(c) Will the terminal p.d. then increase or decrease? (c) Will the terminal p.d. then increase or decrease? Explain your answer. Explain your answer.

V 1.30.2-1.5 t.p.d.

As R increases, the current decreasesAs R increases, the current decreases

The t.p.d. increases because the lost volts will be smaller.The t.p.d. increases because the lost volts will be smaller.


A cell with e.m.f. 1.5 V and internal resistance 2 A cell with e.m.f. 1.5 V and internal resistance 2 is connected is connected to a 3 to a 3 resistor. What is the current? resistor. What is the current?



20

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A pupil is given a voltmeter and a torch battery. When he connects the voltmeter across the terminals A pupil is given a voltmeter and a torch battery. When he connects the voltmeter across the terminals of the battery it registers 4.5 V, but when he connects the battery across a 6 of the battery it registers 4.5 V, but when he connects the battery across a 6 resistor, the voltmeter resistor, the voltmeter reading decreases to 3.0 V. (a) Calculate the internal resistance of the battery.reading decreases to 3.0 V. (a) Calculate the internal resistance of the battery.



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(b) What value of resistor would have to be connected across the (b) What value of resistor would have to be connected across the battery to reduce the voltage reading to 2.5 V ?battery to reduce the voltage reading to 2.5 V ?

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In the circuit shown, the cell has an e.m.f. of 6.0 V and internal resistance of 1 In the circuit shown, the cell has an e.m.f. of 6.0 V and internal resistance of 1 . . When the switch is closed, the reading on the ammeter is 2 A. What is the When the switch is closed, the reading on the ammeter is 2 A. What is the corresponding reading on the voltmeter ?corresponding reading on the voltmeter ?



22

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In order to find the internal resistance of a cell, the In order to find the internal resistance of a cell, the following sets of results were taken.following sets of results were taken.



23

(a) Draw the circuit (a) Draw the circuit diagram used.diagram used.

(b) Plot a graph of these results (b) Plot a graph of these results and from it determine and from it determine (i) the e.m.f. (i) the e.m.f.

(ii) the (ii) the internal resistance of the cell.internal resistance of the cell.

Graph of Voltage against Current

y = -4.1714x + 1.1053

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Current (A)Vo

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23(cont)

(c) Use the e.m.f. from part (b) to calculate the lost volts (c) Use the e.m.f. from part (b) to calculate the lost volts for each set of readings and hence calculate 6 values for for each set of readings and hence calculate 6 values for the internal resistance. the internal resistance.

(d) Calculate the mean value of internal resistance and the (d) Calculate the mean value of internal resistance and the approximate random uncertainty. approximate random uncertainty.

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The voltage across a cell is varied and the corresponding current noted. The The voltage across a cell is varied and the corresponding current noted. The results are shown in the table below. results are shown in the table below. Plot a graph of V against I. Plot a graph of V against I.



24

(b) Calculate the internal (b) Calculate the internal resistance. resistance.

(a) What is the open circuit (a) What is the open circuit p.d? p.d?

Graph of voltage against current

y = -0.1x + 6

5.4

5.5

5.6

5.7

5.8

5.9

6

6.1

6.2

0 1 2 3 4 5 6

Current (A)

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24 cont (c) Calculate the short circuit (c) Calculate the short circuit

current. current.

(d) A lamp of resistance 1.5 (d) A lamp of resistance 1.5 is connected across the is connected across the terminals of this supply. Calculate (i) the terminal p.d.and (ii) terminals of this supply. Calculate (i) the terminal p.d.and (ii) the power delivered to the lamp. the power delivered to the lamp.

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Calculate the p.d. across RCalculate the p.d. across R22 in each case. in each case.



25

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22

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Calculate the p.d. across AB (voltmeter reading) in each Calculate the p.d. across AB (voltmeter reading) in each case.case.



26

Potential at A = 6 VPotential at A = 6 V

Potential at B = 3 VPotential at B = 3 V

p.d. across AB = 3 Vp.d. across AB = 3 V

Potential at A = 2/7 x 5 = 1.4 VPotential at A = 2/7 x 5 = 1.4 VPotential at B = 8/18 x 5 = 2.2 VPotential at B = 8/18 x 5 = 2.2 V

p.d. across AB = - 0.8 Vp.d. across AB = - 0.8 V

Potential at A = 2/5 x 10 = 4 VPotential at A = 2/5 x 10 = 4 V

Potential at B = 4/10 x 10 = 4 VPotential at B = 4/10 x 10 = 4 V

p.d. across AB = 0p.d. across AB = 0


(a) Calculate the reading on the voltmeter.(a) Calculate the reading on the voltmeter.



27

(b) What alteration could be made to balance the bridge (b) What alteration could be made to balance the bridge circuit ?circuit ?

Potential at A = 6/15 x 9 = 3.6 VPotential at A = 6/15 x 9 = 3.6 V

Potential at B = 3/9 x 9 = 3 VPotential at B = 3/9 x 9 = 3 V

p.d. across AB = 0.6 Vp.d. across AB = 0.6 V

Increase the 9 kIncrease the 9 k resistor to 12 k resistor to 12 k


Three pupils are asked to construct balanced Wheatstone Three pupils are asked to construct balanced Wheatstone bridges. Their attempts are shown.bridges. Their attempts are shown.



28

(a) Identify each circuit. (a) Identify each circuit.

One of the circuits gives One of the circuits gives a balanced Wheatstone a balanced Wheatstone bridge, one gives an off bridge, one gives an off - balance Wheatstone - balance Wheatstone bridge and one is not a bridge and one is not a Wheatstone bridge.Wheatstone bridge.

(b) How would you test that balance had been obtained?(b) How would you test that balance had been obtained?

(c) In the off – balance Wheatstone bridge (i) calculate the (c) In the off – balance Wheatstone bridge (i) calculate the potential difference across the galvanometer. potential difference across the galvanometer.

Unbalanced WheatstoneUnbalanced WheatstoneBalanced WheatstoneBalanced WheatstoneNon WheatstoneNon Wheatstone

The galvo should read zero in a balanced Wheatstone BridgeThe galvo should read zero in a balanced Wheatstone Bridge

Potential at A = 5/15 x 1.5 = 0.5 VPotential at A = 5/15 x 1.5 = 0.5 VPotential at B = 10/15 x 1.5 = 1 VPotential at B = 10/15 x 1.5 = 1 V

p.d. across AB = 0.5 Vp.d. across AB = 0.5 VFrom B to AFrom B to A

(ii) in which direction will (ii) in which direction will electric current flow through electric current flow through the galvanometer?the galvanometer?


Calculate the value of the unknown resistor X in each case.Calculate the value of the unknown resistor X in each case.



29

4

3

2

1

RR

RR

9120120

X

9X

4

3

2

1

RR

RR

Xk

kk 12

154

k 454

1512kkkX

4

3

2

1

RR

RR

Xk

kk 6.3

2510

k 910

256.3kkkX


The circuit shown opposite is balanced.The circuit shown opposite is balanced.



30 (a)What is the value of resistance X?(a)What is the value of resistance X?

(b) Will the bridge be unbalanced if (b) Will the bridge be unbalanced if (i) a 5 (i) a 5 resistor is inserted next to the 10 resistor is inserted next to the 10 resistor (ii) a 3 V supply is used.?resistor (ii) a 3 V supply is used.?

(c) What is the function of resistor R and what is the (c) What is the function of resistor R and what is the disadvantage of using it as shown?disadvantage of using it as shown?

4

3

2

1

RR

RR

X5

2010 10X

The bridge will be unbalanced if the resistance is increased to 15 The bridge will be unbalanced if the resistance is increased to 15

The bridge will still be balanced if the supply voltage is changedThe bridge will still be balanced if the supply voltage is changed

The resistor R protects the sensitive galvo from large currents. In The resistor R protects the sensitive galvo from large currents. In series the resistor reduces the sensitivity of the galvo series the resistor reduces the sensitivity of the galvo

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