Two material having the dielectric constants K1 and K2 are filled between two parallel plates of a capacitor. Here area of each plate is A and the distance between the plates is d. The capacity of the capacitor is

Question

Two material having the dielectric constants K1 and K2 are filled between two parallel plates of a capacitor. Here area of each plate is A and the distance between the plates is d. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/0b9973ebbb625317ef58bdc92eb16fc4-.png" /> The capacity of the capacitor is (A) (A ε0(K1 × K2)/d(K1+K2)) (B) (A ε0(K1-K2)/d) (C) (A ε0 K1 K2/(K1+K2)) (D) (A ε0(K1+K2)/d)

Tardigrade Admin · Accepted Answer

In each capacitor, the area of the plate will be

\frac{A}{2}

.
In the given combination, the arrangement is equivalent to two capacitors connected in parallel. Also in each capacitor, the area of the plate will be

\frac{A}{2}

.

∴

Equivalent capacitance,

C^{'} = C_{1} + C_{2}

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

Q. Two material having the dielectric constants $K_{1}$ and $K_{2}$ are filled between two parallel plates of a capacitor.
Here area of each plate is $A$ and the distance between the plates is $d$ .

The capacity of the capacitor is

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

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

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

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

Q. Two material having the dielectric constants K1​ and K2​ are filled between two parallel plates of a capacitor. Here area of each plate is A and the distance between the plates is d. The capacity of the capacitor is

d(K1​+K2​)Aε0​(K1​×K2​)​

dAε0​(K1​−K2​)​

(K1​+K2​)Aε0​K1​K2​​

dAε0​(K1​+K2​)​

Q. Two material having the dielectric constants $K_{1}$ and $K_{2}$ are filled between two parallel plates of a capacitor.
Here area of each plate is $A$ and the distance between the plates is $d$ .

The capacity of the capacitor is

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

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

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

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