Page 81 - Physics 10_Float

ELECTROSTATICS

Q = Q = Q = Q
1
2
3
2. The potential difference across each capacitor is
different due to different values of capacitances.
3. The voltage of the battery has been divided among
the various capacitors. Hence
V = V + V + V 3 Q
2 Q
1 Q
= + + Quick Quiz
C 1 C 2 C 3 Is the equivalent capacitance
1 1 1 of series capacitors larger or
= Q + + smaller than the capacitance
C 1 C 2 C 3
V 1 1 1 of any individual capacitor in
= + + the combination?
Q C 1 C 2 C 3

4. Thus, we can replace series combination of capacitors
with one equivalent capacitor having capacitance C i.e.,
1
1
1
1
eq
= + +
C eq C 1 C 2 C 3
In the case of ‘n’ capacitors connected in series, we have
1
1
1
1
1
.......
=
+
+
+
+
C eq C 1 2 C C 3 C n .......(13.10)
Example 13.4: Three capacitors with capacitances of 3.0 F, µ
4.0 F, and 5.0 F are arranged in series combination to a µ µ
battery of 6V, where 1 F = 10 F. Findµ - 6
(a) the total capacitance of the series combination.

(b) the quantity of charge across each capacitor.

(c) the voltage across each capacitor.

Solution: (a) Diagram is shown on right. For total
C 1 C 2 3 C
capacitance, 1 1 1 1
= + +
C eq C 1 C 2 C 3
1 1 1 1 3.0 F 4.0 F 5.0 Fµ µ µ
= + +
-6
-6
-6
C eq 3.0 x 10 F 4.0 x 10 F 5.0 x 10 F
1 1 1 1 1 K + –
= + + x 6.0 V
C eq 3 4 5 10 F
-6
1 = 47 x 1
C 60 10 F
-6
eq
C = 1.3 µF
eq
(b) In series combination, charge across each capacitor is
same and can be found as:
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