JEE Main202126 Aug 2021Evening ShiftPhysicsCapacitanceActual
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 :
Options
- Aε 0   A   d 1 2 + K 1   K 2   K 1 + K 2
- Bε 0   A   d 1 2 + 2   K 1 + K 2 K 1   K 2
- Cε 0   A   d 1 2 + K 1 + K 2   K 1   K 2
- Dε 0   A   d 1 2 + K 1   K 2 2   K 1 + K 2
Correct answer
A. ε 0   A   d 1 2 + K 1   K 2   K 1 + K 2
Step-by-step solution
C eq = C 1 + C 2 C 3 C 2 + C 3 C eq = A ε 0 2   d + K 1   A ε 0   d × K 2   A ε 0   d K 1   A ε 0   d + K 2   A ε 0   d C eq = A ε 0 2   d + A ε 0   d K 1   K 2   K 1 + K 2 = A ε 0   d 1 2 + K 1   K 2   K 1 + K 2