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MHT CET202525 Apr 2025Evening ShiftPhysicsCapacitanceActual

Seven capacitors each of capacitance 2 ~F are to be connected in a configuration to obtain an effective capacitance ( 10 11 ) F . The combination is

Correct answer

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Step-by-step solution

The effective capacitance of N_p capacitors in parallel and N_s capacitors in series is given by C_ eff = N_p C 1 + N_p N_s . Substituting the given values C = 2 , F and C_ eff = 10 11 , F yields 10 11 = 2N_p 1 + N_p N_s . Using N_p + N_s = 7 , we solve 11N_p = 5(1 + N_p(7 - N_p)) , which simplifies to 5N_p^2 - 24N_p - 5 = 0 . The positive integer solution is N_p = 5 , N_s = 2 , giving C_ eff = 5 2 1 + 5 2 = 10 11 , F . Verification of options: Option A ( N_p=4 , N_s=3 ): C_ eff = 8 13 , F Option B ( N_p=3 , N_s=4

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