Question

The effective capacitance of the capacitor shown in the diagram is $(K_1=2,K_2=4,K_3=6)$

• A. 12 ε₀ A/d
• B. 2 ε₀ A/d
• C. 4 ε₀ A/d
• D. ε₀ A/12d

Answer 1

The correct option is C

4 ε₀ A/d

All there capacitors have same p.d, i.e., they are in parallel.

$C_1=\frac{k_1{ϵ}_0\left(\frac{A}{B}\right)}{d}{C}_2=\frac{k_2{ϵ}_0\left(\frac{A}{B}\right)}{d}{C}_3=\frac{k_3{ϵ}_0\left(\frac{A}{B}\right)}{d}Ceff=C_1+C_2+C_3=\frac{{ϵ}_{0}A}{3d}(K_1+K_2+K_3)=\frac{{ϵ}_{0}A}{3d}(2+4+6)=\frac{4{ϵ}_{0}A}{d}$