# Exam-style Questions: Capacitors

1. The graph shows how the chanreg of a capacitor varies with the p.d. across the capacitor. Use the graph to find

a) the energy stored by the capacitor when charged to a potential difference of 8 V

energy stored = .................. J

(2 Marks)

b) the capacitance of the capacitor

capacitance = ..................... F

(2 Marks)

(Marks available: 4)

2. Fig. 7.1 shows a circuit diagram of a capacitor discharging through a resistor. A simple mathematical model of the discharge of the capacitor is shown in Fig. 7.2. It is assumed that the current / is constant over each small time interval, Δt, The process is repeated as shown. Complete the table for the discharge of the 4700μF capacitor. The small time interval used is Δt = 2.0 s. (3 Marks)

(Marks available: 3)

3. In the circuit in Fig. 6.1, the capacitor is charged to a potential difference of 6.0 V. When the switch is moved from A to B , the capacitor discharges through the resistor.

a) Show that the initial value of the discharge current is about 1 mA.

(2 Marks)

b) The time constant RC of the discharge circuit is about 26 s.

Calculate the current in the discharge circuit after the switch has been closed for a time equal to RC.

current = .............. mA

(2 Marks)

(Marks available: 4)

Answer outline and marking scheme for question:

1. a) Sum of the currents = zero (at junction)OR

sum of the currents in = sum of currents out (at junction)

b) Area under graoh (equiv to ½ QV) = ½ x 3.5 x 10-3 x 8 (1 Mark)

= 0.014 J (1 Mark)

(2 Marks)

c) Grad = 3 x 10-3 / 6.8 (for example) (1 Mark) = 4.4 x 10-4 F (1 Mark)

(2 Marks)

(Marks available: 4)

2. First line of table : 2.4 x 10-3, 4.8 x 10-3 (1 Mark)

Second line of table : 2.2 x 10-3, 4.4 x 10-3 (1 Mark)

4.7 x 10-2

(3 Marks)

(Marks available: 3)

3. a) l = V/R = 6/ 5.6 x 103 (1 Mark) = 1.1 x 10-3 A = (about) 1 mA (1 Mark)

(2 Marks)

b) l = 1.1 x 10-3 x e-1 = 1.1 x 10-3 x 0.37 (1 Mark) = 0.4 mA (1 Mark) (accept rule of thumb third, answers using 1 mA and answers using decay equation)

(2 Marks)

(Marks available: 4) 