A parallel - plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1 and K2 of same area A / 2 and thickness d / 2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:

Question

A parallel - plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1 and K2 of same area A / 2 and thickness d / 2 are inserted in the space between the plates. The capacitance of the capacitor will be given by: (A) (ε0 A / d )((1/2)+( K 1 K 2/ K 1+ K 2)) (B) (ε0 A / d )((1/2)+( K 1 K 2/2( K 1+ K 2))) (C) (ε0 A / d )((1/2)+( K 1+ K 2/ K 1 K 2)) (D) (ε0 A / d )((1/2)+(2( K 1+ K 2)/ K 1 K 2))

Tardigrade Admin · Accepted Answer

C texteq =(( A /2) ε0/ d )+( A ε0/ d ) ( K 1 K 2/ K 1+ K 2) =( A ε0/ d )((1/2)+( K 1 K 2/ K 1+ K 2))

Q. A parallel - plate capacitor with plate area A has separation $d$ between the plates. Two dielectric slabs of dielectric constant $K_{1}$ and $K_{2}$ of same area $A /2$ and thickness $d /2$ are inserted in the space between the plates. The capacitance of the capacitor will be given by:

$\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{K _{1} + K _{2}})$

$\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{2 ( K _{1} + K _{2} )})$

$\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{K _{1} + K _{2}}{K _{1} K _{2}})$

$\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{2 ( K _{1} + K _{2} )}{K _{1} K _{2}})$

$C_{eq} = \frac{\frac{A}{2} ε _{0}}{d} + \frac{A ε _{0}}{d} \frac{K _{1} K _{2}}{K _{1} + K _{2}}$
$= \frac{A ε _{0}}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{K _{1} + K _{2}})$

Q. A parallel - plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1​ and K2​ of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:

dε0​A​(21​+K1​+K2​K1​K2​​)

dε0​A​(21​+2(K1​+K2​)K1​K2​​)

dε0​A​(21​+K1​K2​K1​+K2​​)

dε0​A​(21​+K1​K2​2(K1​+K2​)​)