JEE Main 2022 · 30 June · morning · Single correct · +4 / −1
Cₒ is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity εᵣ (as shown in Fig. 2), the new capacitance of the capacitor will be :
- (a) Cₒ/2(1 + ε ᵣ)
- (b) Cₒ + ε ᵣ
- (c) (Cₒε ᵣ)/2
- (d) Cₒ(1 + ε ᵣ)
Answer and solution
Answer (a) Cₒ/2(1 + ε ᵣ)
Solution
Physics sir · 3 steps
The dielectric fills the right half of the plate area, so you have two capacitors side by side, in parallel.
- Read the figure. In Fig. 2 the dielectric runs the full gap d from one plate to the other, but covers only half the plate area. The other half is still air.
- Two capacitors. Each half has area A/2 and separation d. Both halves touch the same two plates, so they share the same potential difference: that is a parallel combination.
C = (ε₀ (A/2))/d + (εᵣ ε₀ (A/2))/d = C₀/2 + (εᵣ C₀)/2
- So. With C₀ = ε₀ A/d, the new capacitance is C = C₀/2(1 + εᵣ), which is option (a).
The idea to keep. Dielectric across the full gap over part of the area: capacitors in parallel, add them. Dielectric over the full area for part of the gap: capacitors in series. Look at which way the slab cuts.
Answer from the NTA final answer key. Solution by PrepWiser.