AQA AS Physics

Topic Questions

5.4 Electromotive Force & Internal Resistance

1a3 marks

The electromotive force, ε is defined by the equation 

            ε = I (R + r) 

State the definition of the following variables and an appropriate unit for each. 

            (i)         I 

            (ii)        R 

            (iii)       r

1b5 marks

Figure 1 shows a circuit connecting a cell with internal resistance to a resistor. 

Figure 1

5-4-s-q--q1b-easy-aqa-a-level-physics

Place in each of the grey boxes one of the following variables: 

V

r

ε

I

R

1c3 marks

A current of 0.6 mA flows through the circuit in Figure 1 and the resistor has a resistance of 2.5 kΩ. 

Calculate the terminal potential difference of the circuit.

1d3 marks

The internal resistance of the cell is 1.3 kΩ. 

Calculate the emf of the cell.

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2a1 mark

Explain what is meant by the electromotive force of a cell.

2b1 mark

Explain what is meant by the internal resistance of a cell.

2c2 marks

A simple circuit is shown in Figure 1 where a high resistance voltmeter is used to measure the potential difference across the terminals of a battery.

Figure 1

5-4-s-q--q2c-easy-aqa-a-level-physics

State what happens to the voltmeter reading when the switch is closed and explain what this tells us about the battery. 

2d1 mark

Explain why the voltmeter reading changes when the switch is closed.

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3a1 mark

Define, in words, the term lost volts

3b1 mark

Define lost volts in terms of an equation.

3c2 marks

Fran is given the following equipment: 

Voltmeter

Variable resistor

Lamp

Cell

Wires

 

She is asked by her physics teacher to use the equipment to determine the emf of the cell.

Sketch a circuit diagram of the circuit used to determine the emf of the cell. 

You may use a piece of equipment once, more than once or not at all.

3d3 marks

Fran calculates the emf of the cell to be 26.3 V. The total potential difference across the other components in the circuits is 24.0 V.

Calculate the lost volts. State your answer to an appropriate number of significant figures.

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4a3 marks

Figure 1a shows a circuit with a battery of emf ε and internal resistance r connected in series to a variable resistor with resistance R. 

Figure 1a

5-4-s-q--q4a-fig-1-easy-aqa-a-level-physics

A student wishes to determine the relationship between the voltmeter and ammeter readings whilst decreasing R. Table 1 shows the terminal potential difference V and current I read from the voltmeter and ammeter respectively. 

Table 1

Terminal potential difference / V

Current / A

8.3

0.07

6.8

0.17

4.6

0.33

2.9

0.44

0.3

0.63

 

Plot a graph of the data in Table 1 on Figure 1b. 

Figure 1b

5-4-s-q--q4a-fig-2-easy-aqa-a-level-physics

4b2 marks

From Figure 1b, determine the value of ε. Explain your method.

4c4 marks

From Figure 1b, calculate the value of r. Show your method clearly.

4d4 marks

Sketch a line on Figure 1b to show the results obtained from a cell with: 

            (i)         The same emf but larger internal resistance. Label this A. 

            (ii)        The same internal resistance but larger emf. Label this B.

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5a5 marks

Figure 1 is a circuit used to test a battery of 4 identical cells. A 0.62 kΩ resistor is also connected in series with the cell. 

Figure 1

5-4-s-q--q5a-easy-aqa-a-level-physics

A current of 4.50 mA travels through the circuit and the emf of the battery is 2.80 V. 

Calculate the internal resistance of the battery. State an appropriate unit for your answer. 

5b2 marks

Calculate the internal resistance of one cell.

5c2 marks

Calculate the emf of the battery if there was no internal resistance.

5d2 marks

Calculate the difference between the emf of the battery with and without internal resistance and state the significance of this.

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1a2 marks

A uniform wire of length 80 cm and radius 0.50 mm is connected in series with a cell of e.m.f. 3.0 V and an internal resistance of 0.70 Ω as shown in Figure 1. 

Figure 1

5-4-s-q--q1a-hard-easy-aqa-a-level-physics

The resistivity of the metal used to make the wire is 1.1 × 10–6 Ω m. 

Determine the current that flows in the cell.

1b4 marks

A voltmeter is connected at X, with a movable probe C, such that the voltmeter is able to read the potential difference across the wire at different points between X and Y, as shown in Figure 2a.  

Figure 2a

5-4-s-q--q1b-hard-easy-aqa-a-level-physics

Sketch a graph on the set of axes provided in Figure 2b which shows how the potential difference V varies between X and Y as the sliding contact C moves from X to Y. 

Figure 2b

5-4-s-q--q1b-fig-2-hard-easy-aqa-a-level-physics

Your sketch should include all appropriate labels.

1c4 marks

The voltmeter in Figure 2a is replaced with a cell of e.m.f. 1.5 V and internal resistance 0.50 Ω and an ammeter as shown in Figure 3. 

Figure 3

5-4-s-q--q1c-hard-easy-aqa-a-level-physics

The moveable contact can again be connected to any point along the wire XY. 

At point D, there is zero current in the ammeter. 

Calculate the length of XD.

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2a4 marks

Figure 1 shows a circuit which can be used to find investigate the internal resistance r of a power supply. In this case, a battery consisting of six dry cells in series, each of e.m.f. epsilon = 0.5 V, is connected to an oscilloscope:   

Figure 1a

5-4-s-q--q2a-fig-1-hard-easy-aqa-a-level-physics

Figure 1b represents the trace shown on the oscilloscope screen when both of the switches S subscript 1 and S subscript 1 are open:

Figure 1b

5-4-s-q--q2a-fig-2-hard-easy-aqa-a-level-physics

The vertical sensitivity of the oscilloscope is set at 1.5 V div–1. 

With reference to Figure 1b, discuss what happens to the trace shown on the oscilloscope screen when switch S subscript 1 is closed.  

2b3 marks

Use Figure 1b to draw the trace on the oscilloscope screen when both switches S subscript 1 and S subscript 2 are closed. 

Explain your answer.

2c3 marks

Calculate the internal resistance of the battery if the vertical distance between the traces in part (b) and part (c) is measured to be half a division

2d2 marks

Determine the current in the cell that would move the trace shown on the oscilloscope screen back to its original position shown in Figure 1b. 

Assume both switches S subscript 1 and S subscript 2 remain closed.

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3a3 marks

The Maximum Power Transfer theorem says the maximum amount of electrical power is dissipated in a load resistance R subscript L when it is exactly equal to the internal resistance of the power source r. 

Figure 1a shows a circuit used to investigate maximum power transfer. A variable resistor, which acts as the load resistance R subscript L, is connected to a power source of e.m.f. epsilon and internal resistance r, along with a switch S and an ammeter and voltmeter: 

Figure 1a

5-4-s-q--q3a-fig-1-hard-aqa-a-level-physics

Figure 1b shows the graph obtained for the power P dissipated in RL as the potential difference V across R subscript L is varied: 

Figure 1b

5-4-s-q--q3a-fig-2-hard-aqa-a-level-physics

Assuming the Maximum Power Theorem is valid, use Figure 1b to determine the internal resistance of the power source.

3b3 marks

Hence, show that the e.m.f. of the power supply is 9 V.

3c3 marks

Identify what happens to each of the following quantities as the value of the load resistance R subscript L becomes infinitely large:         

i)       Current

ii)      Potential difference across R subscript L

iii)     Power dissipated in R subscript L

3d3 marks

It can be shown that the power P dissipated in the load resistance R subscript L is zero when the load resistance is zero.

Using this, together with the result of the Maximum Power Theorem given in part (a) and your answer to part (c)(iii), sketch a graph on the axes provided in Figure 2 to show how the power dissipated P varies with load resistance R subscript L.

Label the position of the internal resistance, r. 

Figure 2

5-4-s-q--q3d-hard-aqa-a-level-physics

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4a5 marks

Understanding the properties of e.m.f. and internal resistance can help the design decisions of architects and electrical engineers. 

In an experiment to investigate power dissipation across two lamps L1 and L2, an engineer connects them in a series circuit to a cell of e.m.f. 45 V and internal resistance 7 Ω. This is shown in Figure 1: 

Figure 1

5-4-s-q--q4a-hard-aqa-a-level-physics

The lamps L1 and L2, have a resistance of 10 Ω and 25 Ω respectively. 

Calculate the percentage difference between the power generated by the cell and the power dissipated in the two lamps L1 and L2. 

Suggest a reason for this percentage difference.

4b6 marks

The engineer wishes to maximise the power dissipated across each lamp and explores various alternatives to the circuit shown in Figure 1 

Suggest and explain, using appropriate calculations, how the engineer should arrange the lamps L1 and L2 such that the power dissipated in each lamp is maximised.

4c3 marks

The engineer comes up with a theoretical problem, which involves arranging a large number of identical lamps in parallel with each other, as illustrated in Figure 2 below. 

Figure 2

5-4-s-q--q4c-hard-aqa-a-level-physics

The lamps in Figure 2 are connected to a cell of e.m.f. epsilon and internal resistance r. 

Discuss the effect on the terminal pd supplied by the cell, and hence on the lamps in Figure 2, as more lamps are added in parallel.

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1a3 marks

Calculate the internal resistance of a single cell.

1b3 marks

One of the cells in the battery is reversed.     

Determine the new reading on the ammeter in circuit Y.

1c4 marks

In circuit Y, the resistance of the load resistor R is altered so that a series of values on the voltmeter and the corresponding values of the current on the ammeter are obtained. 

Figure 2

5-4-s-q--q1d-medium-easy-aqa-a-level-physics

Using the axes in Figure 2, sketch the graph you would expect to obtain as R is changed. State how the values of ∈ and r can be obtained from the graph.

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2a4 marks

A battery of e.m.f. 30.0 V and internal resistance, r, is connected in the circuit shown in Figure 1. 

Figure 1

5-4-s-q--q2a-medium-easy-aqa-a-level-physics

The current in the battery is 1.5 A. 

Calculate the internal resistance r.

2b2 marks

Calculate the energy dissipated in the battery in 3.0 minutes.

2c2 marks

Calculate the percentage of the total energy transformed by the battery that is dissipated in the battery in 3.0 minutes.

2d3 marks

The internal resistance of the battery affects the efficiency of the transfer of energy from the battery to the circuit. 

Explain what causes internal resistance and why this affects the efficiency.

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3a3 marks

A cell of e.m.f., ∈, and internal resistance, r, is connected to a variable resistor R. The current through the cell and the terminal p.d. of the cell are measured as R is decreased. The circuit is shown in Figure 1 below.

Figure 1

5-4-s-q--q3a-fig-1-medium-easy-aqa-a-level-physics

The graph in Figure 2 below shows the results from the experiment. 

Figure 2

5-4-s-q--q3a-fig-2-medium-easy-aqa-a-level-physics

State the relationship between the terminal pd and current and explain why this relationship occurs.

3b4 marks

Use the graph in Figure 2 to find the e.m.f., ∈, and the internal resistance, r, of the cell.

3c2 marks

Draw a line on the graph in Figure 2 that shows the results obtained from a cell with the same e.m.f. but half the internal resistance of the first cell. Label your graph A.

3d1 mark

Draw a line on the graph in Figure 2 that shows the results obtained from a cell with the same e.m.f. but negligible internal resistance. Label your graph B.

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4a2 marks

A battery is connected to an 8.0 Ω resistor as shown in Figure 1 below. The e.m.f. of the battery is 15 V. 

Figure 1

5-4-s-q--q4a-medium-easy-aqa-a-level-physics

When the switch is open the voltmeter reads 15 V and when it is closed it reads 14.3 V. 

Explain why the readings are different.

4b3 marks

Calculate the internal resistance of the battery.

4c2 marks

The circuit diagram in Figure 2 shows that the 8.0 Ω resistor is now connected in parallel with an unknown resistor, R. The battery now supplies a current of 2.0 A and has the same internal resistance r as the circuit in Figure 1. 

Figure 2

5-4-s-q--q4c-medium-easy-aqa-a-level-physics

Calculate the p.d. across the 8.0 Ω resistor.

4d3 marks

Calculate the resistance of R

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5a3 marks

A very high resistance voltmeter reads 10.5 V when it is connected across the terminals of a power supply. 

Explain why the reading on the voltmeter is equal to the emf of the power supply.

5b2 marks

A battery of e.m.f. 10.5 V and internal resistance r is connected in a circuit as shown in Figure 1 with three identical 15 Ω resistors. A current of 0.30 A flows through the battery. 

Figure 1

5-4-s-q--q5b-medium-easy-aqa-a-level-physics

Calculate the potential difference between points A and B in the circuit.

5c3 marks

Calculate the internal resistance of the battery.

5d3 marks

Calculate the fraction of the energy supplied by the battery that is dissipated within the battery in 5.0 s.

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