MHT CET202526 Apr 2025Morning ShiftPhysicsCapacitanceActual
The capacity of air filled parallel plate capacitor is C ₀ . One-half of the space between the plates is filled with a dielectric constant ' K ' as shown in figure. The new capacity becomes C_n . The ratio C_n to C₀ is
Options
- A( K +1 2 )
- B( K +1 3 )
- C( K +1 4 )
- D4(K+1)
Correct answer
A. ( K +1 2 )
Step-by-step solution
The capacitance of the air-filled parallel plate capacitor is C₀ = ₀ A d . When one-half of the space is filled with dielectric constant K while the other half remains air-filled, the configuration becomes equivalent to two parallel capacitors. The dielectric-filled portion has capacitance C₁ = K ₀ (A/2) d = K 2 C₀ , and the air-filled portion has C₂ = ₀ (A/2) d = 1 2 C₀ . The total new capacitance is C_n = C₁ + C₂ = K 2 C₀ + 1 2 C₀ = C₀ ( K+1 2 ) . The ratio C_n C₀ = K+1 2 . Final answer: K+1 2