A parallel plate capacitor with air as medium between the plates has a capacitance 10 mF. The area of the capacitor is divided into two equal halves and filled with two media having dielectric constants K₁ = 2 and K₂ = 4. The capacitance of the system will be

Complete Solution:

A parallel plate capacitor with air as the medium has a capacitance of 10 mF. The area of the capacitor is divided into two equal halves, filled with dielectric constants K₁ = 2 and K₂ = 4. Let's calculate the new capacitance.

Capacitance Formula:

C = (ε₀ K A) / d, where:

C: Capacitance

K: Dielectric constant

A: Area of the plates

d: Distance between plates

ε₀: Permittivity of free space

Since the plate is divided into two halves with different dielectrics, the system behaves like two capacitors connected in parallel.

Effective Capacitance in Parallel: C_total = C₁ + C₂

Step-by-Step Calculation

Original Capacitance: The air-filled capacitor has a total capacitance of 10 mF.

Area of Each Half: Since the area is equally divided: A₁ = A₂ = A / 2

Capacitance of Each Half:

For the first half (K₁ = 2):

C₁ = (ε₀ K₁ A₁) / d = (ε₀ × 2 × A / 2) / d = 10 mF

For the second half (K₂ = 4):

C₂ = (ε₀ K₂ A₂) / d = (ε₀ × 4 × A / 2) / d = 20 mF

Total Capacitance: Since the halves are in parallel:

C_total = C₁ + C₂ = 10 mF + 20 mF = 30 mF

Final Answer

The capacitance of the system is 30 mF.