Consider the battery of constant voltageE0 that charges the capacitor shown in FIGURE

Chapter 4, Problem 35

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Consider the battery of constant voltageE0 that charges the capacitor shown in FIGURE 4.3.9. Divide equation (20) by Land define 2,\ = RIL and w2 = l/LC. Use the Laplace transform to show that the solution q(t) of q" + 2,\q' + w2q = E0/L, subject to q(O) = 0, i(O) = 0, is E0c[ 1 - e-At(coshVA2 - w2t + V A sinhVA.2 - w21)] . A> w ,\2 _ w2 q(t) = E0c[ 1 - e-At(l + A t)] . A = w E0c[ 1 - e-.1.{ cos V w2 - A.2t + V A sin V w2 - A2t)] . ,\. < w.

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