Capacitance (Edexcel A Level Physics): Structured Questions

The properties of capacitors make them useful in timing circuits.

The following circuit is used to provide an input Y to an integrated circuit.

Initially, the capacitor is uncharged. The switch S₁ is closed. 

Sketch a graph to show how the potential at point Y varies with time.

When the potential at Y is 8.0 V, the switch S₂ is closed.

i) Calculate the time taken for the potential at Y to decrease to 2.0 V.

Time taken = ......................................................(3)

ii) Calculate the energy stored on the capacitor when the potential at Y is 2.0 V.

Energy stored = ......................................................(2)

When the potential at Y is 2.0 V, the switch S₂ is opened.

Calculate the power dissipated by the resistance R₁ when the potential at Y is 2.0 V.

Power dissipated = ......................................................

A ‘Gauss gun’ can be made from five ball bearings of equal mass and two magnets, as shown.

Pairs of ball bearings are placed to the right of two strong magnets. A single ball bearing is released from the left, as shown. The ball bearing is attracted to, and collides with, the first magnet. This and all subsequent collisions can be assumed to be elastic.

Explain what happens to make the last ball bearing on the right subsequently move off with a large velocity.

A student set up the apparatus shown to measure the speed of the last ball bearing.

The ‘Gauss gun’ was placed at the end of a bench, so that the ball bearing left the gun and broke two strips of metal foil which formed part of an electric circuit.

As the ball bearing left the gun, it broke the first foil strip at its centre so that the capacitor started to discharge. When the ball bearing broke the second foil strip the capacitor discharge stopped.

i) Calculate the energy stored in the capacitor when it was fully charged.

Energy stored = ................................(2)

ii) The voltmeter reading halved in the time taken for the ball bearing to travel between the two foil strips.

Show that the time taken for the ball bearing to travel between the two foil strips was about 0.1 s.

(2)

iii) The two foil strips were 0.50 m apart.

Calculate the horizontal velocity of the ball bearing.

Horizontal velocity = ..................................(2)

iv) The student positioned the second foil strip with its centre 8.0 cm lower than the centre of the first foil strip.

Deduce whether the ball bearing broke the second foil strip at its centre.

Assume the ball bearing was travelling horizontally as it broke the first foil strip.

(2)

An emergency lighting system uses the capacitor circuit shown.

When the mains power is on, the two-way switch is connected to position X to charge the capacitor. The capacitor is uncharged at time $t=0\text{ s}$.

(i) Explain how the current in the circuit varies when the switch is connected to position X.

[3]

(ii) Complete the graph to show how the current varies with time until the capacitor is fully charged.

Include values on both axes.

[4]

When the mains power fails, the switch connects to position Y and the capacitor discharges through the $250\text{ kΩ}$ resistor.

Show that the time taken for the capacitor to lose 99% of its full charge is approximately $\text{17}$ times longer than the time taken to reach 99% of its full charge.

An external sensor circuit monitors the potential difference (p.d.) across the capacitor. An LED warning light in the sensor circuit remains switched on as long as the p.d. remains above $2.0\text{ V}$.

The LED is required to stay on for at least $15\text{ minutes}$ after a power failure.

Deduce whether the design of the circuit meets this requirement.

An emergency exit sign uses a supercapacitor as a backup power supply for its lamp unit. The circuit is shown.

During normal operation, the switch is in position X and the capacitor is fully charged. If there is a power cut, the switch moves to position Y and the capacitor discharges through the lamp unit, keeping the sign lit.

When the sign is first installed, the capacitor is uncharged. The switch is moved to position X and the capacitor charges through the lamp unit.

Sketch, on the axes below, the variation of the charging current with time. Include the value of the initial current.

Calculate the energy stored in the capacitor when it is fully charged.

capacitance of capacitor = $22\text{ F}$

p.d. across the capacitor when fully charged = $5.0\text{ V}$

Show that the time constant of the discharge circuit is about $1500\text{ s}$.

resistance of lamp unit = $68\text{ Ω}$

Determine the p.d. across the lamp unit 15 minutes after a power cut begins.

Safety regulations require the sign to remain lit for at least 15 minutes after a power cut begins. The lamp unit remains lit provided the p.d. across it is at least $2.2\text{ V}$.

Assess whether this capacitor meets the requirement.