Sheet 5
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
6V
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
=
= 5V
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
8. A parallel plate air capacitor is made by using two metallic 16 cm2
plates 4.7 mm apart. It is connected to a 12-V battery. (a) What is the
capacitance? (b) What is the charge on each plate, (c) What is the
energy stored in the capacitor? (d) If the battery is disconnected and
the plates are pulled apart to a separation of 9.4 mm, what are the
answers to (a), (b) and (c)?
c)
d)
c)
9.
10.
Calculate the equivalent capacitor
Since above three highlighted capacitors are in series, so their equivalent capacitance
(Cx) will be:
1/Cx = 1/3 + 1/3 +1/3
1/Cx = 3/3 = 1
Cx = 1μf
After substituting the 1μf instead of three series capacitors, we can see that
now 1μf and 2μf are in parallel, so their equivalent (Cy) will be:
Cy = 1 + 2
Cy = 3μf
Now after further simplification, again three 3μf capacitors are in series, So
their equivalent(Cz) will be:
1/Cz = 1/3 + 1/3 +1/3
1/Cz = 3/3 = 1
Cz = 1μf
Again combination of series capacitors (1μf) and 2μf are in parallel, so their
equivalent(Ct) will be:
Ct = 1 + 2
Ct =3μf
Now finally three capacitors are series so their equivalent will be:
1/C = 1/3 + 1/3 +1/3
1/C = 3/3 = 1
C = 1μf