1. Capacitor Question Practice
A2 Physics

2. Q1 What is the energy held by a 50 000 mF capacitor charged to 12.0 V?
(2 marks)

3. A1
E = ½ CV2
E = ½ × × 10-6 F × (12.0 V)2 (P) = 3.6 J (P)

4. Q2 What is the charge held by a
470 mF capacitor charged to a p.d. of 8.5 V? 
(2 marks)  

5. A2
Q = CV (P)
= 470 x 10-6 F × 8.5 V
= 4.0 × 10-3 C (P)

6. What is the capacitance ofQ3
A capacitor is connected to a 12V power supply by a reed switch operating at 400 Hz.  
The ammeter reads 45 mA.  
What is the capacitance of
the capacitor?
(2 marks)

7. A3 Q = It but f = 1/t so Q = I/f C = Q/V = I ¸ (Vf)
C = A ¸ (400 Hz × 12.0 V) (P)
C = 9.38 × 10-6 F = 9.38 mF (P)

8. Q4
A 5000 mF capacitor is charged to 12.0 V and discharged through a 2000 W resistor.
(a)  What is the time constant? (1 mark)
(b)  What is the voltage after 13 s? (2 marks)
(c)  What is the half-life of the decay? (2 marks)
(d)  How long would it take the capacitor to discharge to 2.0 V (3 marks)
(8 marks total)

9. 4a
   
Time constant = RC 
= 2000 W × 5000 × 10-6 F
= 10 s (P)

10. 4b V = V0 e –t/RC V = 12.0 × e – 13 /10 (P) V = 12.0 × e – 1.3
= 12.0 × 0.273  
= 3.3 volts (P)

11. 4c V = V0 e –t/RC V ¸ V0 = 0.5 = e –t(half)/RC ln(0.5) = - t1/2 /RC
ln2 = t1/2  /RC (P)
(The log of a reciprocal is the negative of that for the original number)
t1/2  = × RC 
= × 10 = 6.93 s (P)

12. (When you divide two numbers, you subtract their logs)
V = V0 e –t/RC 
V  ¸  V0 = e –t/RC
ln V - ln Vo = -t/RC (P)
(When you divide two numbers, you subtract their logs)
0.693 – = - t/10
ln2 - ln12 = - t/10 (P)
-t/10 =
t/10 = 1.792
t = × 10 = 17.9 s (P)