An air filled parallel plate capacitor is to be constructed which can store 12 μC of charge when operated at 1200 V. What can be the minimum area of capacitor? The dielectric strength of air is 3 x 10⁷ V/m.

Solution

Given,
Charge, Q = 12 μC
Potential applied across the capacitor, V = 1200 V
Dielectric strength of air = 3 x 10⁷ V/m
We have to find the minimum area of the capacitor, A.

Since, dielectric strength is the maximum electric field, a material can tolerate without break down. Therfore, for safety let the electric field never exceed ~ 10% of dielectric strength.
That is,
$E = \frac{σ}{\in_{0}} = \frac{Q}{A \in_{0}} = \frac{10}{100} \times 3 \times 10^{7} = 3 \times 10^{6} V / m$

$∴$ minimum area of capacitor is given by, $A = \frac{Q}{\in_{0} \times 3 \times 10^{6}} = \frac{12 \times 10^{- 6}}{8.85 \times 10^{- 12} \times 3 \times 10^{6}} = 0.45 m^{2}$

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An air filled parallel plate capacitor is to be constructed which can store 12 μC of charge when operated at 1200 V. What can be the minimum area of capacitor? The dielectric strength of air is 3 x 10⁷ V/m.

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An air filled parallel plate capacitor is to be constructed which can store 12 μC of charge when operated at 1200 V. What can be the minimum area of capacitor? The dielectric strength of air is 3 x 10⁷ V/m.