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How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?
Sol. q = Q(1 – e^-n) 1/2 Q^2/C = Initial value ; 1/2 q^2/c = Final value 1/2 q^2/c * 2 = 1/2 Q^2/C ⇒ q^2 = Q^2/2 ⇒ q = Q/√2 Q/√2 = Q(1 – e^-n) ⇒ 1/√2 = 1 – e^-n ⇒ e^-n 1 - 1/√2 ⇒ n = log(√2/√2 - 1) = 1.22
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