RP 9: Investigation of the charge and discharge of capacitors. Analysis techniques should include log-linear plotting leading to a determination of the time constant, RC.

What is the method used to investigate the discharge of a capacitor through a resistor? (6)

- Set up a circuit with a battery, resistor, capacitor, switch, and voltmeter connected in series.

- Close the switch to allow the capacitor to charge fully to the battery voltage.

- Open the switch and immediately start a stopwatch.

- Record the voltage across the capacitor every 5 seconds as it discharges.

- Continue recording until the voltage has dropped close to zero.

- Repeat the experiment two more times and calculate the mean voltage at each time point.

What equipment is required to investigate the discharging of a capacitor? (5)

- Capacitor.

- Resistor.

- Battery.

- Voltmeter.

- Switch.

What does a setup used to investigate the discharge of a capacitor through a resistor look like? (3)

What is the independent variable in the discharging capacitor experiment? (1)

The independent variable is the time after the capacitor starts discharging.

What is the dependent variable in the discharging capacitor experiment? (1)

The dependent variable is the voltage across the capacitor.

What are the controlled variables in the discharging capacitor experiment? (3)

- The controlled variables include the initial voltage.

- Another controlled variable is the resistance in the circuit.

- Another controlled variable is the capacitance of the capacitor.

What graph is used to determine the time constant in the capacitor discharging experiment? (1)

Plot a graph of ln(V) against time (t) using the measured voltages.

What does the graph used to determine the time constant in the capacitor discharging experiment look like? (3)

What does the gradient of the ln(V) against time graph represent? (2)

- The gradient of the straight line will be equal to -1/RC.

- Where R is the resistance and C is the capacitance.

How is the time constant calculated from the discharging graph? (1)

Calculate the time constant τ using the equation τ = -1 ÷ gradient.

What is one safety precaution in the discharging capacitor experiment? (1)

Ensure the capacitor is connected with the correct polarity and its voltage rating is not exceeded, to prevent the risk of explosion or leakage of harmful chemicals.

How can the exponential decay be shown clearly in the capacitor experiment? (1)

Plot a graph of voltage (V) against time (t) as well as ln(V) against t to show the exponential decay directly.

How else can the time constant τ be determined in the discharge experiment? (1)

Determine the time constant τ by finding the time it takes for the voltage to fall to 37% of its original value.

What is the method used to investigate the charging of a capacitor through a resistor? (5)

- Set up a circuit containing a battery, resistor, capacitor, switch and voltmeter in series.

- Close the switch and begin timing.

- Record the voltage across the capacitor every 5 seconds as it charges.

- Continue recording until the voltage approaches the supply voltage (usually around 120 seconds).

- Repeat the experiment twice more and find the average voltage at each time interval.

What equipment is required to investigate the charging of a capacitor? (5)

- Capacitor.

- Resistor.

- Battery.

- Voltmeter.

- Switch.

What does a setup used to investigate the charging of a capacitor through a resistor look like? (3)

What is the independent variable in the capacitor charging experiment? (1)

The independent variable is the time after the capacitor begins charging.

What is the dependent variable in the capacitor charging experiment? (1)

The dependent variable is the voltage across the capacitor.

What are the controlled variables in the capacitor charging experiment? (3)

- The controlled variables include the battery voltage.

- Another controlled variable is the resistance in the circuit.

- Another controlled variable is the capacitance of the capacitor.

What graph is plotted in the capacitor charging experiment to find the time constant? (1)

Plot a graph of voltage (V) against time (t).

What does the graph plotted in the capacitor charging experiment to find the time constant look like? (3)

How is the time constant found from the charging graph? (1)

Identify the time when the voltage across the capacitor reaches approximately 63% of the battery voltage.

What formula links the time constant τ to the circuit components? (1)

The time constant τ is equal to the product of resistance (R) and capacitance (C) (τ = RC).

What is one safety precaution when performing the capacitor charging experiment? (1)

Ensure the capacitor is connected with the correct polarity and that its voltage rating is not exceeded, to avoid the risk of explosion or chemical leakage.

What is one improvement for the capacitor charging experiment? (2)

- Repeat the experiment with different combinations of resistance and capacitance

- To investigate how the time constant changes with these values.