Charging and Discharging (CIE A Level Physics)

The variation with potential difference V of the charge Q on one of the plates of a capacitor is shown in Fig. 1.1.

Fig. 1.1

The capacitor is connected to a 12.0 V power supply and two resistors P and Q are shown in Fig. 1.2.

Fig. 1.2

The resistance of P is 28 kΩ and the resistance of Q is 280 kΩ.

The switch can be in either position A or position B.

The switch is in position A so that the capacitor is fully charged.

Calculate the energy E stored in the capacitor.

The switch is now moved to position B.

 Show that the time constant of the charge circuit is 4.2 s.

The fully charged capacitor in (a) stores energy E. 

Determine the time t taken for the stored energy to decrease from E to E/4.

A capacitor of capacitance 520 μF is connected to a battery of electromotive force (e.m.f.) 36 V in the circuit of Fig. 1.1.

Fig. 1.1

The two-way switch is initially at position X.

X and Y are identical long straight wires, each with a resistance of 2.4 kΩ. These wires are placed near to and parallel to each other. Wire Y is connected to a voltmeter. 

At time t = 0, switch S is moved to position B so that the capacitor discharges through wire X.

Calculate the time constant τ of the discharge circuit.

(i)

On FIg. 1.2, sketch a line to show the variation with t of the current I in wire X as the capacitor discharges. 

 

Fig. 1.2

[2]

 

Fig 1.3

[1]

Explain why there is an induced e.m.f. across wire Y during the discharge of the capacitor.