Question

Two parallel plate air capacitors have the same separation. The plates of the first are squares of side 10 cm. The plates of the second are squares of side 20 cm. The ratio of their capacitance is :

• A. 2 : 1
• B. 1 : 2
• C. 4 : 1
• D. 1 : 4

Answer 1

The correct option is D 1 : 4

We know $C=\frac{{ϵ}_{0}A}{d}$
$\therefore C_1=\frac{{ϵ}_0(10\times {10}^{-2}\times 10\times {10}^{-2})}{d}$
$\therefore C_1=\frac{{ϵ}_0(20\times {10}^{-2}\times 20\times {10}^{-2})}{d}$
$\frac{C_1}{C_2}=\frac{1}{4}$