Examstyle Questions: Capacitors

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)

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)

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:

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)

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)

a) l = V/R = 6/ 5.6 x 10^{3} (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)
