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

This question was posed to me in unit test.

This intriguing question comes from Advanced Problems on Network Theory topic in portion Network Theory and Complex Circuit Diagram of Network Theory

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 \(\frac{∈_1 ∈_2}{∈_1+∈_2}\).