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A parallel plate capacitor is filled by a dielectric whose permittivity varies with applied voltage according to relation $ε_{r} = α V,$ where $α = 1 {(v o l t)}^{- 1}$ . The same capacitor containing no dielectric, charged to a voltage of 72 volt is connected in parallel to the first non-linear uncharged capacitor. The final voltage across the capacitor is

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19V

36V

answer is D.

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Detailed Solution

$V_{c o m m o n} = \frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} + C_{2}}$

Here let $C_{1} = C V, C_{2} = C$ . $C$ is the capacitance of capacitor without dielectric.

On solving we get $V_{c o m m o n} = 8 V$

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