AIIMS2017PhysicsCapacitance
A parallel plate capacitor with air as a dielectric has capacitance C . A slab of dielectric constant K , having same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be
Options
- A(K+3) C 4
- B(K+2) C 4
- C(K+1) C 4
- DK C 4
Correct answer
A. (K+3) C 4
Step-by-step solution
The two condensers with K and with air are in parallel. With air, C₁= ₀ d ( 3 A 4 )= 3 ₀ A 4 d With medium, C₂= ₀ K d ( A 4 )= ₀ A K 4 d C^ =C₁+C₂ or C^ = 3 ₀ A 4 d + ₀ A K 4 d = ₀ A d [ 3 4 + K 4 ] or C^ = C 4 (K+3) [ C= A ₀ d ]