Question

A network of four capacitors of capacity equal to c1 = c, c2 = 2c, c3 = 3c and c4 = 4c are

Answer 1

$\bold{\frac{3}{22}}$ is the ratio of charges on c2 and c4.

Solution:

There are capacitors c1, c2, c3 and c4 are in the series, which is in the attachment below,

$\frac{1}{c}=\frac{1}{c}+\frac{1}{2 c}+\frac{1}{3 c}$

$\frac{1}{c}=\frac{6+3+2}{6 c}$

$\frac{1}{c}=\frac{11}{6 c}$

$\mathrm{K}=\frac{6 c}{11}$

All three capacitors are on the same branch. Hence all are in series, now the charges on each of the capacitors are given by $Q^{\prime}=\frac{6 c}{11}$

Now the charge on capacitor C4 is given by $\mathrm{Q}=4 \mathrm{CV}$

So ratio of Q’ and Q is $=\frac{Q^{\prime}}{Q}$

$=\frac{6 C V}{11 \times 4 C V}$

$=\frac{3}{22}$

The charge ratio of c2 and c4 is $\frac{3}{22}.$