Differential Equations Quiz
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An RLC circuit with resistance R=3ΩR=3\Omega, inductance L=1HL=1\text{H}, and capacitance C=0.5FC=0.5\text{F} is governed by the equation Lq′′+Rq′+1Cq=E(t)Lq'' + Rq' + \frac{1}{C}q = E(t). If the circuit starts with zero charge and zero current, and a constant voltage of E(t)=10VE(t) = 10\text{V} is applied at time t=2st=2\text{s}, what is the charge q(t)q(t) on the capacitor for t>0t>0?
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