Page 80 - Physics 10_Float

ELECTROSTATICS

Quick Quiz
In the case of ‘n’ capacitors connected in parallel, the Is the equivalent capacitance
equivalent capacitance is given by of parallel capacitors larger or
smaller than the capacitance
C = C + C + C + ……. + C …….(13.9) of any individual capacitor in
1
eq
n
3
2
5. The equivalent capacitance of a parallel combination the combination?
of capacitors is greater than any of the individual
capacitances.
c 1
Example 13.3: Three capacitors with capacitances of 3.0 , µF
4.0 , and 5.0 are arranged in parallel combination with a µF µF
battery of 6 V, where 1 = 10 F. FindµF -6 c 2
(a) the total capacitance
(b) the voltage across each capacitor c 3
(c) the quantity of charge on each plate of the
capacitor
Solution: Diagram is shown on right.
(a) Total capacitance is given by
C = C + C + C V = 6 V
eq 1 2 3
-6
-6
-6
C eq = 3.0 x10 F +4.0 x10 F + 5.0 x10 F
-6
-6
C = (3+4+5) x10 F = 12 x 10 F
eq
C = 12 µF
eq
(b) As three capacitors are connected in parallel, Energy Stored in a Capacitor
the voltage across each capacitor will Capacitor stores energy in an
electric field between two
be same and is equal to the voltage of the
plates in the form of
battery i.e., 6 V. electrostatic potential energy.
(c) Charge on a capacitor with capacitance C
1
Q = C V
1
1
- 6
-6
Q 1 = 3.0 x 10 F x 6 V = (3x6) x10 F V
Q = 18 µC
1
Similarly, charge on capacitors with capacitances C and
2
C is 24 and 30 respectively.µC µC
3
(ii) Capacitors in Series C 1 C 2 3 C
+Q –Q +Q –Q +Q –Q
In this combination, the capacitors are connected side by side
i.e., the right plate of one capacitor is connected to the left
plate of the next capacitor (Fig. 13.15). This type of + –
K
combination has the following characteristics: V
1. Each capacitor has the same charge across it. If the Fig.13.15: capacitors in series
battery supplies + Q charge to the left plate of the capacitor C 1, combination.
due to induction – Q charge is induced on its right plate and +Q
charge on the left plate of the capacitor C i.e.,
2
80 Not For Sale – PESRP