An air-filled parallel plate capacitor has a capacitance C₀ . The separation between the plates is d . A dielectric slab of thickness d 2 and dielectric constant K is introduced between the plates. If the new capacitance becomes 4 3 C₀ , the value of K is:

Step-by-step solution

The capacitance of an air-filled parallel plate capacitor is C₀ = ₀A d . When a dielectric slab of thickness t and dielectric constant K is inserted, the new capacitance is given by: C = ₀A d - t + t K Given t = d 2 and C = 4 3 C₀ : 4 3 C₀ = ₀A d - d 2 + d 2K 4 3 C₀ = ₀A d 2 + d 2K 4 3 C₀ = C₀ 1 2 + 1 2K 1 2 + 1 2K = 3 4 1 2K = 3 4 - 1 2 = 1 4 2K = 4 K = 2 Answer: 2