First slide

Capacitance

Question

The effective capacitance of two capacitors of capacitances C₁^' and C₂^' (with ${C_{2}}^{'} > {C_{1}}^{'}$ ) connected in parallel is 25/6 times the effective capacitance when they are connected in series. The ratio $\frac{C_{2}^{'}}{C_{1}^{'}}$ is :

Moderate

A

$\frac{3}{2}$
B

$\frac{4}{3}$
C

$\frac{5}{3}$
D

$\frac{25}{6}$

Solution

$C_{1}^{'} + C_{2}^{'} = \frac{25}{6} (\frac{C_{1}^{'} C_{2}^{'}}{C_{1}^{'} + C_{2}^{'}}) \Rightarrow 6 {(C_{1}^{'} + C_{2}^{'})}^{2} = 25 C_{1}^{'} C_{2}^{'} \Rightarrow 6 C_{1}^{' 2} + 6 C_{2}^{' 2} - 13 C_{1}^{'} C_{2}^{'} = 0 . . . (1) Let C_{2}^{'} = {xC}_{1}^{'} eqn . (1) becomes 6 x^{2} - 13 x + 6 = 0 x = 3 / 2 or \frac{2}{3} Since C_{2}^{'} > C_{1}^{'} x = \frac{2}{3} is not possible .$

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