A parallel plate capacitor has capacitance C. If it is equally filled the parallel layers of materials of dielectric constant K1 and K2 its capacity becomes C1. The ratio of C1 and C is

Question

A parallel plate capacitor has capacitance C. If it is equally filled the parallel layers of materials of dielectric constant K1 and K2 its capacity becomes C1. The ratio of C1 and C is (A) K1 + K2  (B) (K1 K2/K1 + K2) (C) (K1 + K2/K1 K2) (D) (2 K1 K2/K1 + K2)

Tardigrade Admin · Accepted Answer

CA = (K1 ε0A/(d)2) , CB = (K2ε0A/(d)2) Ceq = (C1/C2) = (2K1K2/K1 + K2) = (CACB/CA + CB) = ((2K1 K2/K1 + K2)) (ε0A/d) ( ∵ e = (ε0A/d))

Q. A parallel plate capacitor has capacitance $C$ . If it is equally filled the parallel layers of materials of dielectric constant $K_{1}$ and $K_{2}$ its capacity becomes $C_{1}$ . The ratio of $C_{1}$ and $C$ is

$K_{1} + K_{2}$

$\frac{K _{1} K _{2}}{K _{1} + K _{2}}$

$\frac{K _{1} + K _{2}}{K _{1} K _{2}}$

$\frac{2 K _{1} K _{2}}{K _{1} + K _{2}}$

Q. A parallel plate capacitor has capacitance C. If it is equally filled the parallel layers of materials of dielectric constant K1​ and K2​ its capacity becomes C1​. The ratio of C1​ and C is

K1​+K2​

K1​+K2​K1​K2​​

K1​K2​K1​+K2​​

K1​+K2​2K1​K2​​

CA​=2d​K1​ε0​A​,CB​=2d​K2​ε0​A​ Ceq​=C2​C1​​=K1​+K2​2K1​K2​​ =CA​+CB​CA​CB​​=(K1​+K2​2K1​K2​​)dε0​A​ (∵e=dε0​A​)

Q. A parallel plate capacitor has capacitance $C$ . If it is equally filled the parallel layers of materials of dielectric constant $K_{1}$ and $K_{2}$ its capacity becomes $C_{1}$ . The ratio of $C_{1}$ and $C$ is

$K_{1} + K_{2}$

$\frac{K _{1} K _{2}}{K _{1} + K _{2}}$

$\frac{K _{1} + K _{2}}{K _{1} K _{2}}$

$\frac{2 K _{1} K _{2}}{K _{1} + K _{2}}$