Question

Derive an expression for capacitance of parallel plate capacitor partially filled with dielectric of dielectric constant K

Answer 1

★ Answer :

→ Refer to the attachment.

Answer 2

Expression for capacitance of parallel plate capacitor with partially filled dielectric material:

The intensity of the electric field is given as:

E₀ = σ/ε₀

Electric field intensity within the dielectric medium is given as:

E = σ/Kε₀

The potential difference between the plates is given as:

V = E₀ × (d - t) + Et

On substituting the required values, we get,

V = σ/ε₀ × (d - t) + σ/Kε₀ × t

V = σ/ε₀ [(d - t) + t/K]

V = q/Aε₀ [(d - t) + t/K]

The capacitance of the condenser is given as:

C = q/V

∴ C = Aε₀/((d - t) + t/K)