Capacitance (Edexcel International A Level (IAL) Physics): Structured Questions

A student built the circuit shown. The capacitor was initially uncharged.

She closed the switch and plotted a graph of current on ammeter A₁ against time.

Determine whether the initial value of current on the graph is consistent with the values stated on the circuit diagram.

Explain how the current on ammeter A₂ would vary over the same time interval.

Determine the capacitance of the capacitor.

Capacitance = ...............................

Determine the charge stored on the capacitor after 30 s.

Charge stored on capacitor after 30 s = ................................

Determine the maximum energy stored by the capacitor.

Maximum energy = ...............................

The train on a model railway is powered by contact with the rails. The train sometimes loses contact with the rails. The diagram shows a circuit that can maintain power for an electronic controller on the train even when the power is disconnected for a short time.

The switch represents the contact between the train and the rails.

Explain how this circuit can maintain power to the electronic controller if the switch is opened for a short time.

The switch is opened.

Calculate the time taken for the potential difference across the capacitor to decrease to 4.0 V.

Assume the resistance of the electronic controller is infinite.    

capacitance of capacitor = 47 mF    

resistance of resistor = 470 Ω

Time taken = ...........................................

The switch is closed at time t = 0 and then opened at t = 20 s.

Sketch a graph on the axes below to show how current I through the resistor varies with t.

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.