Question

D is the distance between the plates of a parallel plate capacitor. The dielectric constants are ∈1 and ∈2 respectively. The total capacitance is proportional to ____________

(a) \(\frac{∈_1 ∈_2}{∈_1+∈_2}\)

(b) ∈1 – ∈2

(c) \(\frac{∈_1}{∈_2}\)

(d) ∈1 ∈2

Answer 1

Right choice is (a) \(\frac{∈_1 ∈_2}{∈_1+∈_2}\)

Easiest explanation: The combination is equal to two capacitors in series.

So, C = \(\frac{\Big[∈_0 ∈_1 \left(\frac{A}{0.5d} \right)\Big]\Big[∈_0 ∈_2 \left(\frac{A}{0.5d} \right)\Big]}{∈_0 ∈_1  \frac{A}{0.5d} + ∈_0 ∈_1  \frac{A}{0.5d}}\)

Hence, C is proportional to \(\frac{∈_1 ∈_2}{∈_1+∈_2}\).