Lesson 3.1
Capacitance
1.
Capacitance
As a conductor gets charged, its potential increases. The amount of charge
given to a conductor to increase its potential by 1 volt is called the
capacitance of the conductor. We use C to represent capacitance. Since
capacitance is charge per unit volt,
Q
C
V
=
Since Q is measured in coulombs and V is measured in volts, C is measured
in coulombs per volt (C.V
1
) and is called a farad (F). Since farad is a very
large unit we very often use microfarad (
μ
F = 10
6
F), nanofarad (nF = 10
9
F) and picofarad (pF = 10
12
F) which are the submultiples of a farad.
You have seen earlier that the potential of a spherical conductor which
carries a charge Q is
R
Q
R
kQ
V
0
4
πε
=
=
Therefore, capacitance of a spherical conductor can be written as
0
0
4
/ 4
Q
Q
C
R
V
Q
R
πε
πε
=
=
=
…1
Example 1
:
An isolated spherical conductor of radius 10 cm is charged to
2.0 kV. (a) How much charge is on the conductor? (b) What is the
capacitance of the sphere? (c) How does the capacitance change if the sphere
is charged to 6.0 kV?
Solution:
(a)
The capacitance of a spherical conductor
C = 4
πε
o
R
=
4
π
×
8.85
×
10
12
×
0.1
= 1.1
×
10
11
F = 11 pF
But
V
Q
C
=
.
Q = C V = 1.1
×
10
11
×
2.0
×
10
3
= 2.2
×
10
8
C =
22 nC
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(b)
C =
11 pF
(c)
C does not depend on the amount of charge or the potential of the
conductor, it only depends on the physical dimensions of the
conductor. In order to raise the voltage to 6.0 kV, there is a
proportional increase in the amount of charge on the conductor.
Therefore, the ratio Q/V will remain the same. The capacitance is still
11 pF
2.
Capacitor.
+
+
+
+
+
+
+
C=Q/V
+
+
+
+
+
+
+









+
+
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+
(a)
(b)
Fig. 1
neutral
conductor
+
+
+
+
+
+









grounded
(c)
Fig. 1(a) shows a conductor carrying a charge Q so that its potential is V
volts. The capacitance of the conductor is given by
V
Q
C
=
. Fig 1(b) shows a
neutral conductor brought near the charged conductor. The negative charges
in the neutral conductor move so that they reside closer to the positively
charged conductor making the other end of the neutral conductor positive.
The accumulation of negative charges near the positively charged object
lowers its positive potential to V’ so that V’ < V. This decrease in potential
of the charged conductor without changing the amount of charge on it causes
an increase in its capacitance. In order to increase the potential back to V,
more positive charges need to be given to the conductor. Thus the presence
of a neutral conductor near the charged conductor raises the capacitance of
the charged conductor. If now the neutral conductor is grounded, the positive
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 Spring '11
 George
 Physics, Capacitance, Charge, Electric charge, Coaxial cable, 3 m, μF, 6 mm, Qmax

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