# Answers to Problems - The Capacitor

1. What is the charge stored when the voltage across a 50 μF capacitor is 9 V?

Q  =  VC  =  9 V  ×  50 μF  =  450 μF

2. What is the capacitance of a capacitor that stores 12 μC of charge when connected to a 6 V battery?

 C  = Q = 12 μC =  2 μC V 6 V

3. Work out the voltage across the plates of a 10 μF capacitor when it has a charge of 50 μC.

 V  = Q = 50 μC =  5 V C 10 μF

4. Calculate the energy stored in a capacitor with a charge of 200 μC and 9 V across its plates.

 W  =  ½ QV  = 200 μC  ×  9 V =  0.9 mJ 2

5. Calculate the energy stored in a 1 μF capacitor charged to 50 V.

 W  =  ½ V 2C  = 2500 V  ×  1 mF =  1.25 mJ 2

6. What is the combined capacitance of:

a) a 2.2 μF capacitor and a 4.7 μF capacitor in parallel?

CTOTAL  =  C1  +  C2  =  2.2 μF  +  4.7 μF  =  6.9 μF

b) two 100 μF capacitors in series?

 CTOTAL  = C1  ×  C2 = 10,000 μF =  50 μF C1  +  C2 200 μF

7. What is the total combined capacitance of the network shown below?

 CTOTAL  = C1  ×  (C2  +  C3) = 5 μF  ×  25 μF =  4.167 μF C1  +  (C2  +  C3) 30 μF