AQA AS Physics

Topic Questions

5.3 Circuits & The Potential Divider

1a2 marks

A student wishes to investigate how resistance behaves in an electric circuit. Specifically, they are interested in how the total resistance depends on whether the resistors are arranged in series or in parallel. 

They set up a circuit of four identical resistors, each of resistance 5 Ω, as shown in Figure 1:

Figure 1

5-3-s-q--q1a-easy-aqa-a-level-physics

The internal resistance of the cell is negligible. 

Calculate the total resistance of the circuit shown in Figure 1.

1b3 marks

The student rearranges the same set of resistors in a circuit with the same cell, as shown in Figure 2

Figure 2

5-3-s-q--q1b-easy-aqa-a-level-physics

Calculate the total resistance of the circuit shown in Figure 2

1c1 mark

State what the student should conclude about the total resistance in a series circuit compared to the total resistance in a parallel circuit.

1d2 marks

The student proposes an extension to the experiment, in order to verify their conclusion about total resistance. 

They suggest including an ammeter next to the cell in Figure 1 and in Figure 2, such that a measurement of total current in each circuit can be taken. This is shown in Figure 3. 

Figure 3

5-3-s-q--q1d-easy-aqa-a-level-physics

State and explain which ammeter in Figure 3, A1 or A2, shows a larger current.

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2a1 mark

State Kirchhoff’s First Law.

2b3 marks

A network of three identical resistors and three ammeters is set up. 

One of the ammeters reads 3.5 A, as shown in Figure 1: 

Figure 1

5-3-s-q--q2b-easy-aqa-a-level-physics

Hence, or otherwise, determine the currents shown on: 

   (i)     A1 

   (ii)    A2

2c1 mark

State the conservation law for which Kirchhoff’s First Law is a direct consequence.

2d1 mark

State another quantity that is conserved in all electric circuits.

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3a3 marks

Figure 1 shows two resistors, R­1 and R2, connected in series with a battery of emf 6.0 V and negligible internal resistance. 

Figure 1

5-3-s-q--q3a-easy-aqa-a-level-physics

The reading on the voltmeter is 4.0 V and the resistance of R1 is 60 Ω. Calculate:  

(i)
The current in the circuit 
(ii)
The resistance of R2

3b2 marks

In the circuit shown in Figure 1, resistor R2 is replaced with a resistor R­­3 of resistance 240 Ω, as shown in Figure 2

Figure 2

5-3-s-q--q3b-easy-aqa-a-level-physics

Calculate the reading on the voltmeter across R3

3c1 mark

In the circuit shown in Figure 2, resistor R1 is now replaced with an LDR. 

State what happens to the reading on the voltmeter as the incident light on the LDR gets brighter.

3d4 marks

Calculate the power transmitted by the cell in Figure 2 if the current through it is 20 mA. 

State an appropriate unit with your answer.

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4a5 marks

A filament lamp A is rated at 60 W 230 V. 

A different type of lamp B is promoted as having the same light intensity output, but is rated as 12 W 230 V. 

Calculate the electrical energy converted by each lamp if both are left on for 2 hours over a period of 31 days.

4b2 marks

State and explain which lamp wastes more thermal energy.

4c2 marks

Show that the standard unit of power, the Watt W, is equivalent to one Joule per second.

4d3 marks

The lamps described in part (a) are installed in a home, which runs off of main electricity at 230 V. 

A simplified circuit of the setup is shown in Figure 1:

Figure 1

5-3-s-q--q4d-easy-aqa-a-level-physics

Calculate the electrical resistance caused by lamp A operating at 60 W.

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5a2 marks

Figure 1 shows a circuit containing a battery of emf 14.0 V, two resistors, a light-dependent resistor (LDR), an ammeter and a switch S. The battery has negligible internal resistance. 

Figure 1

5-3-s-q--q5a-easy-aqa-a-level-physics

When the switch S is open, calculate the potential difference between the points X and Y.

5b3 marks

The switch S is now closed. 

The ambient light in the environment around the circuit in Figure 1is such that the resistance of the LDR is 50 Ω. 

Calculate the total resistance of the LDR and the 10.0 Ω resistor between X and Y.

5c2 marks

Hence, or otherwise, calculate the total resistance in the circuit.

5d2 marks

Hence, calculate the reading on the ammeter.

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1a4 marks

Figure 1 shows a current I = 10 A flowing into a network of resistors: 

Figure 1

5-3-s-q--q1a-hard-aqa-a-level-physics

The potential difference across XY is 8 V. 

Calculate the value of the unknown resistance R.

1b3 marks

Figure 2 shows another network of resistors connected to a 6 V battery with negligible internal resistance. 

Figure 2

5-3-s-q--q1b-ma-hard-aqa-a-level-physics

Each resistor is identical and has a fixed resistance of 2 Ω. 

Determine the reading on the ammeter in Figure 2.

1c6 marks

Another network of resistors is set up to form a ‘resistor cube’, such as that shown in Figure 3: 

Figure 3

5-3-s-q--q1c-hard-aqa-a-level-physics

Each of the resistors are identical and have a resistance of 2 Ω. 

Determine the current that flows in the circuit if A and B in Figure 3 are connected to the terminals of a 6 V power supply.

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2a2 marks

Ohm’s law describes the relationship between voltage and current for a metal conductor at constant temperature. The power transmission of ohmic conductors has important electrical properties. 

Sketch a graph on the axes provided in Figure 1 to show the relationship between power P and current I in an Ohmic component. 

Figure 1

5-3-s-q--q2a-hard-aqa-a-level-physics

2b3 marks

A student wishes to investigate how to maximise the power generated in a load of two resistors, connected to a fixed power supply of negligible internal resistance. 

They try different combinations of two resistors from four available, as shown in Figure 2, and they also try different ways to connect them. 

Figure 2

5-3-s-q--q2b-hard-aqa-a-level-physics

Determine which two resistors the student should select and draw on Figure 2 how the resistors should be connected in the circuit. 

Justify your answer without performing any calculations. 

2c2 marks

Figure 3 shows another method the student comes up with for varying the resistance of the load in the circuit.

Figure 3

5-3-s-q--q2c-hard-aqa-a-level-physics

The four resistors are connected in a loop with sockets A, B, C and D at each junction. Two leads are used to connect the resistor loop to X and Y. 

Determine the resistance of the load if one of the leads connects X and A and the other lead connects Y and C in Figure 3.

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3a3 marks

A circuit is set up as shown in Figure 1 below: 

Figure 1

5-3-s-q--q3a-hard-aqa-a-level-physics

The cells in Figure 1 have negligible internal resistance. 

R subscript 1 is a variable resistor with a resistance that varies between 0 and 10 Ω, and R subscript 2  and R subscript 3  are fixed resistors with a resistance of 10 Ω and 30 Ω respectively. 

Initially,  is set such that its resistance is 0 Ω. 

By labelling the direction of current on Figure 1, write down the relationship between three currents I subscript 1 I subscript 2  and I subscript 3  at the junction between R subscript 1  and R subscript 2 .

3b4 marks

Determine the current through the resistor R subscript 2 .

3c4 marks

State and explain what happens to the potential difference across R subscript 2  as the resistance of R subscript 1  is gradually increased from zero.

3d6 marks

Calculate the current flowing through each resistor when R1 is set to a resistance of 10 Ω.

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4a2 marks

Varying the potential difference across components can be achieved in several different ways in electric circuits. 

Potentiometers are devices that can vary an output potential difference (pd). Potentiometers consist of a sliding contact which can move along a wire. If connections are made across one end of the wire and the sliding contact, the output pd can be varied. 

Figure 1a shows a potentiometer in action. The wire in the potentiometer is represented by a fixed resistor of resistance 10 Ω and the sliding contact C can move from one end of the wire (at position P) to the other end of the wire (position Q). The potentiometer is in series with another fixed resistor of 5 Ω. 

Figure 1a

5-3-s-q--q4a-hard-aqa-a-level-physics

This circuit is powered by a 9 V power supply and is used to supply a variable potential difference (pd) to another circuit. 

Sketch a graph on the axes provided in Figure 1b to show how the supplied pd V varies as the moving contact C is moved from position P to position Q.

Figure 1b

5-3-s-q--q4a-fig-1-hard-aqa-a-level-physics

4b4 marks

Potential divider circuits generally comprise of two or more resistors in series with each other. 

Some potential divider circuits have multiple branches connected in parallel, such as that shown in Figure 2: 

Figure 2

5-3-s-q--q4b-hard-aqa-a-level-physics

Show that the potential difference between X and Y is 1 V.

4c3 marks

A wire joins X and Y in the potential divider circuit in Figure 2. 

Based on your reasoning in part (b), deduce and explain whether a conventional current flows from X to Y or from Y to X.

4d3 marks

Figure 3 shows another potential divider circuit which includes a thermistor with resistance R. 

Figure 3

5-3-s-q--q4d-hard-aqa-a-level-physics

The battery has an EMF of 12 V, with negligible internal resistance. At room temperature, the resistance of the thermistor is 5 kΩ.

Calculate the current in the battery at room temperature.

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1a2 marks

A student is given four resistors of resistance 4.0 Ω, 5.0 Ω, 2.5 Ω and 6.0 Ω respectively. 

Draw the arrangement, using all four resistors, which will give the largest resistance and calculate the resistance of this arrangement.

1b3 marks

Draw the arrangement, using all four resistors, which will give the smallest resistance and calculate the resistance of this arrangement.

1c2 marks

The four resistors are now connected to a battery of emf 12 V and negligible internal resistance, as shown in Figure 1. 

Figure 1

5-3-s-q--q1c-medium-aqa-a-level-physics

Calculate the total resistance in the circuit.

1d4 marks

The circuit is now modified to the one shown in Figure 2. 

Figure 2

5-3-s-q--q1d-medium-aqa-a-level-physics

Calculate the voltage across the 3.0 Ω resistor.

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2a3 marks

In Figure 1 below the battery, of negligible internal resistance, has an emf of 40 V. The p.d. across the lamp is 4.0 V and its resistance is 6 Ω. 

Figure 1

5-3-s-q--q2a-medium-aqa-a-level-physics

Calculate the total resistance of the circuit.

2b2 marks

Calculate the potential difference between points A and B.

2c2 marks

Show that the power of the lamp is about 3 W.

2d2 marks

What percentage of the total power supplied is dissipated in the lamp?

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3a2 marks

Figure 1 shows a potential divider consisting of a fixed resistor in series with a light dependent resistor (LDR). The voltmeter connected in parallel with the light dependent resistor has an infinite resistance. The battery has an emf of 20 V with a negligible internal resistance. 

Figure 1

5-3-s-q--q3a-medium-aqa-a-level-physics

Calculate the reading on the voltmeter when the light dependent resistor has a resistance of 1350 Ω.   

3b3 marks

The voltmeter is now connected in parallel with the fixed resistor as shown in Figure 2. 

Figure 2

5-3-s-q--q3b-medium-aqa-a-level-physics

The light intensity in the room is increased. 

State and explain what happens to the resistance of the LDR and the reading on the voltmeter.

3c4 marks

The circuit in Figure 2 is used as a simple light sensing circuit. When the voltmeter reading falls below 7.5 V, this acts as a signal which switches on a safety lamp when it is dark. 

Calculate the minimum resistance of the LDR for the safety light to come on when it is dark.

3d2 marks

The LDR has a resistance of 15.5 Ω when fully illuminated. 

Calculate the value on the voltmeter when the LDR is fully illuminated.

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4a3 marks

The circuit shown in Figure 1 can be used as an electronic thermometer. The battery has negligible internal resistance. 

Figure 1

5-3-s-q--q4a-medium-aqa-a-level-physics

The reading on the digital voltmeter can be converted to give the temperature of the thermistor T which is used as a temperature sensor. 

Explain what happens to the reading on the voltmeter as the temperature of the thermistor decreases.

4b3 marks

The graph shown in Figure 2 shows how the resistance of the thermistor varies with temperature. 

Figure 2

5-3-s-q--q4b-medium-aqa-a-level-physics

The reading on the voltmeter is 2.9 V when thermistor T has a temperature of 80°C. 

Calculate the potential difference of the battery.

4c2 marks

Calculate the current in the circuit when thermistor T has a temperature of 80°C.

4d2 marks

Calculate the power that has to be removed from the thermistor T to maintain the temperature at 80°C. 

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5a2 marks

Figure 1 below shows a bulb connected in a circuit with two resistors, an ammeter and a battery of emf 25 V and negligible internal resistance. 

Figure 1

5-3-s-q--q5a-medium-aqa-a-level-physics

The current through the ammeter is 15.0 mA. 

Calculate the p.d. across the 1850 Ω resistor.

           

5b2 marks

Calculate the resistance of the parallel combination of the resistor and the bulb.

5c3 marks

Calculate the resistance of the bulb.

5d3 marks

The bulb is replaced with another identical bulb with lower resistance. 

State and explain what happens to the p.d. across the 1850 Ω resistor.

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