Circuits & The Potential Divider (AQA A Level Physics)

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.

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

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

Figure 1

Calculate the total resistance in the circuit.

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

Figure 2

Calculate the voltage across the 3.0 Ω resistor.

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

Calculate the total resistance of the circuit.

Calculate the potential difference between points A and B.

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

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

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

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

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

Figure 2

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.

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.

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

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

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

Figure 1

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.

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

Figure 2

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.

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

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

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

The current through the ammeter is 15.0 mA. 

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

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

Calculate the resistance of the bulb.

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.

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

Figure 1

The potential difference across XY is 8 V. 

Calculate the value of the unknown resistance R.

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

Figure 2

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

Determine the reading on the ammeter in Figure 2.

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

Figure 3

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.

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

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

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. 

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

Figure 3

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.

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

Figure 1

The cells in Figure 1 have negligible internal resistance. 

 is a variable resistor with a resistance that varies between 0 and 10 Ω, and  and  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 ,   and  at the junction between  and .

Determine the current through the resistor .

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

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

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

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

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

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

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.

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

Figure 3

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.