# Worksheet: Variable Resistors in Voltage Divider Circuits

In this worksheet, we will practice calculating the voltages and currents in voltage divider circuits that contain variable resistors.

**Q1: **

The circuit in the diagram shown contains a variable resistor and a negative temperature coefficient thermistor. The variable resistor is connected in parallel with a heating element.

What is the potential difference across the heating element?

If the temperature changes and the resistance of the thermistor increases to 2.6 kΩ, what is the potential difference across the heating element?

If the temperature changes and the resistance of the thermistor decreases to 96 Ω, what is the potential difference across the heating element?

**Q2: **

A voltage divider circuit with a 12 V battery contains a 65 Ω fixed resistor and a variable resistor. The power dissipated by the fixed resistor is 37.5 mW. What is the resistance of the variable resistor set to?

**Q3: **

The circuit in the diagram shown contains a variable resistor and a negative temperature coefficient thermistor.

What would the reading on the voltmeter be?

What would the resistance of the thermistor have to be for the voltmeter to read 20 V?

**Q4: **

The graph shows the change in the resistance of a negative temperature coefficient thermistor with its temperature.

What is the temperature increase from an initial temperature of that reduces the resistance of the resistor by a factor of two?

What is the ratio of the resistances of the resistor at temperatures of and ?

**Q5: **

The graph shows the change in the potential difference across a thermistor with the resistance of the thermistor in a potential divider circuit with a variable resistor. A 15 V battery is used in the circuit.

Which line on the graph corresponds to the variable resistor having the greatest resistance?

- ALine V
- BLine III
- CLine IV
- DLine I
- ELine II

What is the lowest value that is used for the resistance of the variable resistor?

What is the value of the resistance of the variable resistor that produces line III?

**Q6: **

The circuit in the diagram contains a variable resistor and a negative temperature coefficient thermistor. The resistance of the variable resistor is lowered while the temperature of the thermistor changes. The voltmeter reading decreases when this happens. Which of the following statements correctly describes how the temperature of the thermistor could have changed?

- AThe temperature could have increased or decreased.
- BThe temperature must have decreased.
- CThe temperature must have increased.

**Q7: **

The circuit in the diagram shown contains a variable resistor and a negative temperature coefficient thermistor. The graph shown plots the change in the resistance of the thermistor with its temperature.

What is the thermistor’s temperature to the nearest degree?

- A
- B
- C
- D
- E

What would be the reading on the voltmeter if the temperature of the thermistor was ?

- A28 V
- B0 V
- C12 V
- D17 V
- E20 V

**Q8: **

The graph shows the change in the potential difference across a thermistor with the resistance of the thermistor, in a potential divider circuit with a variable resistor.

The circuit is used as a sensor that controls a thermostat. Which line on the graph corresponds to the sensor that is the least sensitive to changes in temperature?

- ALine I
- BLine III
- CLine IV
- DLine V
- ELine II

The circuit is used to directly provide power to a heater. Which line corresponds to the circuit that can supply the least heating power?

- ALine III
- BLine V
- CLine I
- DLine IV
- ELine II

**Q9: **

A voltage divider circuit is constructed and it contains a potentiometer with a maximum resistance of 1.6 kΩ and a thermistor. The lengths and are the distances between the potentiometer’s mobile contact and its fixed contacts, as shown in the diagram.

What is the resistance of the thermistor?

What is the current through the thermistor?

**Q10: **

A voltage divider circuit is constructed such that it contains a light-dependent resistor (LDR) and a 750 Ω fixed resistor. When the light shining on the LDR changes wavelength, the resistance of the circuit changes as shown in the graph. What is the resistance of the LDR when the light shining on it has a wavelength of 600 nm?