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Capacitor
problems
1. A 470 F capacitor is charged by a 20V
cell and then discharged across a 530 
resistor.
a) Draw a suitable circuit to achieve this.
b) Show that the time constant for the
discharge circuit is 0.25 s.
c) Show that the units of the time constant
are seconds (s).
d) Show that the p.d. across the capacitor
has fallen to 7.4 V after 0.25 s.
e) Plot a graph to show the p.d. across the
capacitor after 0.25, 0.50 and 0.75 s.
Answers:
a) Suitable circuit to include cell, capacitor,
2-way switch, Voltmeter across the
capacitor.
b) Time constant = RC = 530 x 470 x 10-6 =
0.249 s.
c) Use Q/Qo = e-t/RC to show RC is in s.
d) After one “RC”, p.d. has dropped by e:
20/e = 20/2.7 = 7.4V
e) After 0.50 s, V= 7.4/e = 2.7 V. After
0.75 s,V = 2.7/e = 1.0 V. Plot suitable
graph.
2. Use the circuit below for this question:
Cell: 6.0V
A
B
Capacitor: 4700 F
Resistor: 5.6 k 
a) When the switch is moved from A to B, what will
happen to the capacitor current?
b) Show the initial value of the current is about
1mA.
c) What is the time constant of the circuit?
d) What is the current flowing in the circuit after
the switch has been closed for a time equivalent
to 2 x RC.
Answers:
a) The current will move in the opposite
direction to the charging current, and through
the resistor as the capacitor DISCHARGES.
b) Since I =V/R, I is 6/5600 = 1.1 x 10-3 A
c) Time constant = RC = 4700 x 10-6 x 5.6 x
103 = 26.3 s.
d) After 2 x RC seconds, I will be 1.1mA/e2 =
1.1/7.29 = 0.15 mA.
3. A capacitor is used to make a light flash on and off
at regular intervals. The capacitor is marked 4700
F and is attached to a 100 V cell and a resistor.
a) Find the charge on the capacitor.
b) If the time constant of the circuit is 0.70s, what is
the value of the resistor in the circuit?
c) When the capacitor charges and reaches 72V, the
lamp switches on. What is the energy stored in the
capacitor?
d) When the lamp flashes, it transfers energy at an
average rate of 150 W.What is the duration of the
flash?
e) Draw a suitable circuit to show how the lamp can be
switched on and off. Include all components.
Answers:
a) Q = CV = 4700 x 10-6 x 100 = 0.47 C
b) 0.70 = 4700 x 10-6 x R. So R = 150 
c) E = ½ CV2 = ½ x 4700 x 10-6 x 72 x 72 =
12.2 J
d) t = 12.2/150 = 0.08 s
e) Suitable circuit includes capacitor and lamp
in parallel with R, switch and cell in series.