An uncharged parallel plate capacitor filled with a dielectric of dielectric constant K is connected to an air filled identical parallel capacitor charged to potential V1. If the common potential is V2, the value of K is

Question

An uncharged parallel plate capacitor filled with a dielectric of dielectric constant K is connected to an air filled identical parallel capacitor charged to potential V1. If the common potential is V2, the value of K is (A) (V1-V2/V1) (B) (V1/V1-V2) (C) (V2/V1-V2) (D) (V1-V2/V2)

Tardigrade Admin · Accepted Answer

Here, V2 =((C V1+0)/(C+K C)) V2 =(V1/1+K) (V2/V1) =(1/1+K) 1+K =(V1/V2) K =(V1/V2)-1 k =(V1-V2/V2)

Q. An uncharged parallel plate capacitor filled with a dielectric of dielectric constant $K$ is connected to an air filled identical parallel capacitor charged to potential $V_{1}$ . If the common potential is $V_{2}$ , the value of $K$ is

$\frac{V _{1} - V _{2}}{V _{1}}$

$\frac{V _{1}}{V _{1} - V _{2}}$

$\frac{V _{2}}{V _{1} - V _{2}}$

$\frac{V _{1} - V _{2}}{V _{2}}$

$\frac{V _{1} - V _{2}}{V _{1} + V _{2}}$

Here,
$V_{2} = \frac{( C V _{1} + 0 )}{( C + K C )}$
$V_{2} = \frac{V _{1}}{1 + K}$
$\frac{V _{2}}{V _{1}} = \frac{1}{1 + K}$
$1 + K = \frac{V _{1}}{V _{2}}$
$K = \frac{V _{1}}{V _{2}} - 1$
$k = \frac{V _{1} - V _{2}}{V _{2}}$

Q. An uncharged parallel plate capacitor filled with a dielectric of dielectric constant K is connected to an air filled identical parallel capacitor charged to potential V1​. If the common potential is V2​, the value of K is

V1​V1​−V2​​

V1​−V2​V1​​

V1​−V2​V2​​

V2​V1​−V2​​

V1​+V2​V1​−V2​​

Here, V2​=(C+KC)(CV1​+0)​ V2​=1+KV1​​ V1​V2​​=1+K1​ 1+K=V2​V1​​ K=V2​V1​​−1 k=V2​V1​−V2​​