A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is

Question

A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is (A)  2 C  (B)  C/2  (C)  (1+K)C/2  (D)  2C(1+K)

Tardigrade Admin · Accepted Answer

The dielectric is introduced such that, half of its area is occupied by it. In the given case the two capacitors are in parallel.

∴ C^{'} = C_{1} + C_{2}

C_{1} = \frac{A ε _{0}}{2 d}

and

C_{2} = \frac{K A ε _{0}}{2 d}

Thus,

C^{'} = \frac{A ε _{0}}{2 d} + \frac{K A ε _{0}}{2 d}

C^{'} = \frac{C}{2} (1 + K)

Q. A dielectric of dielectric constant $K$ is introduced such that half of its area of a capacitor of capacity $C$ is occupied by it. The new capacity is

$2 C$

$C /2$

$(1 + K) C /2$

$2 C (1 + K)$

Q. A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is

2C

C/2

(1+K)C/2

2C(1+K)

The dielectric is introduced such that, half of its area is occupied by it. In the given case the two capacitors are in parallel. ∴C′=C1​+C2​ C1​=2dAε0​​ and C2​=2dKAε0​​ Thus, C′=2dAε0​​+2dKAε0​​ C′=2C​(1+K)

Q. A dielectric of dielectric constant $K$ is introduced such that half of its area of a capacitor of capacity $C$ is occupied by it. The new capacity is

$2 C$

$C /2$

$(1 + K) C /2$

$2 C (1 + K)$