Question

A parallel plate capacitor is filled by a di-electric whose relative permitivity varies with the applied voltage according to the law = $\alpha V$, where $\alpha$ = 1 per volt. The same (but containing no di-electric) capacitor charged to a voltage $V=156volt$ is connected in parallel to the first "non-linear" uncharged capacitor. Determine the final voltage (in volts) $V_f$ across the capacitors is $2\times X$. The value of $x$ is:

Answer 1

So, $Q=CV$

$Q=156C$

thus,

$q_1+q_2=156C$

$CV+\alpha C{V}^2=156C$

$V^2+V-156=0$ [$\alpha =1$ per volt (given)]

$\Rightarrow V=12Volts$