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 Select the correct answer from above options network theory questions and answers, network theory questions pdf, network theory question bank, network theory gate questions and answers pdf, mcq on network theory pdf, gate network theory questions and solutions, network theory mcq Test , ies network theory questions, Network theory Questions for GATE EC Exam, Network Theory MCQ (Multiple Choice Questions)

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} .