A parallel plate capacitor has the space between its plates filled by the two slabs of thickness (d/2) each and dielectric constants K1 and K2, d is the plate separation of the capacitor. The capacity of the capacitor is

Question

A parallel plate capacitor has the space between its plates filled by the two slabs of thickness (d/2) each and dielectric constants K1 and K2, d is the plate separation of the capacitor. The capacity of the capacitor is (A) (2 ε0 d/A)((K1+K2/K1 K2)) (B) (2 ε0 A/d)((K1 K2/K1+K2)) (C) (2 ε0 A/A)(K1+K2) (D) (2 ε0 A/d)((K1+K2/K1 K2))

Tardigrade Admin · Accepted Answer

C1=(K1 ε0 A/d / 2)=(2 K1 ε0 A/d) and C2=(2 K2 ε0 A/d) ∴ (1/Cs)=(1/C1)+(1/C2)=(d/2 K1 ε0 A)+(d/2 K2 ε0 A) =(d/2 ε0 A)((K1+K2/K1 K2)) ⇒ Capacity, Cs=(2 ε0 A/d)((K1 K2/K1+K2))

Q. A parallel plate capacitor has the space between its plates filled by the two slabs of thickness $\frac{d}{2}$ each and dielectric constants $K_{1}$ and $K_{2}, d$ is the plate separation of the capacitor. The capacity of the capacitor is

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

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

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

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

Q. A parallel plate capacitor has the space between its plates filled by the two slabs of thickness 2d​ each and dielectric constants K1​ and K2​,d is the plate separation of the capacitor. The capacity of the capacitor is

A2ε0​d​(K1​K2​K1​+K2​​)

d2ε0​A​(K1​+K2​K1​K2​​)

A2ε0​A​(K1​+K2​)

d2ε0​A​(K1​K2​K1​+K2​​)

C1​=d/2K1​ε0​A​=d2K1​ε0​A​ and C2​=d2K2​ε0​A​ ∴Cs​1​=C1​1​+C2​1​=2K1​ε0​Ad​+2K2​ε0​Ad​ =2ε0​Ad​(K1​K2​K1​+K2​​) ⇒ Capacity, Cs​=d2ε0​A​(K1​+K2​K1​K2​​)

Q. A parallel plate capacitor has the space between its plates filled by the two slabs of thickness $\frac{d}{2}$ each and dielectric constants $K_{1}$ and $K_{2}, d$ is the plate separation of the capacitor. The capacity of the capacitor is

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

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

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

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