An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air cored parallel capacitor charged to a potential V. The two capacitors share charges and the common potential is V' . The dielectric constant K is

Question

An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air cored parallel capacitor charged to a potential V. The two capacitors share charges and the common potential is V' . The dielectric constant K is (A) (V'-V/V'+V) (B) (V'-V/V') (C) (V'-V/V) (D) (V-V'/V')

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9e14cd099fda92b190331b732d343293-.png" /> V'=((K C)(0)+(C)(v)/K C+C) V'=(C V/K C+C) K V'+V'=V K V'=V'-V' K=(V-V'/V')

Q. An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air cored parallel capacitor charged to a potential $V$ . The two capacitors share charges and the common potential is $V^{'} .$ The dielectric constant $K$ is

$\frac{V ^{'} - V}{V ^{'} + V}$

$\frac{V ^{'} - V}{V ^{'}}$

$\frac{V ^{'} - V}{V}$

$\frac{V - V ^{'}}{V ^{'}}$

$V^{'} = \frac{( K C ) ( 0 ) + ( C ) ( v )}{K C + C}$
$V^{'} = \frac{C V}{K C + C}$
$K V^{'} + V^{'} = V$
$K V^{'} = V^{'} - V^{'}$
$K = \frac{V - V ^{'}}{V ^{'}}$

Q. An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air cored parallel capacitor charged to a potential V. The two capacitors share charges and the common potential is V′. The dielectric constant K is

V′+VV′−V​

V′V′−V​

VV′−V​

V′V−V′​