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Question: A network of four capacitors of capacity equal to C<sub>1</sub> = C, C<sub>2</sub> = 2C, C<sub>3</su...

A network of four capacitors of capacity equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C are conducted to a battery as shown in figure. The ratio of the charges on C2 and C4 is:

A

3/22

B

7/4

C

22/3

D

4/7

Answer

3/22

Explanation

Solution

C ' = eq. of (C1, C2 & C3)

1C′=1C+12C+13C\frac { 1 } { \mathrm { C } ^ { \prime } } = \frac { 1 } { \mathrm { C } } + \frac { 1 } { 2 \mathrm { C } } + \frac { 1 } { 3 \mathrm { C } }Ž

C' = 6C11\frac { 6 \mathrm { C } } { 11 }

\ = 4CV ; qC2\mathrm { q } _ { \mathrm { C } _ { 2 } } = 6CV11\frac { 6 \mathrm { CV } } { 11 }

\ qC2qC4=6CV11×4CV=322\frac { q _ { C _ { 2 } } } { q _ { C _ { 4 } } } = \frac { 6 C V } { 11 \times 4 C V } = \frac { 3 } { 22 }