Physic Labs

Problem 2

A capacitor CC initially carrying charge Q0Q_0 is connected at t=0t=0 to a resistor RR. Find charge Q(t)Q(t), current I(t)I(t), and total heat dissipated by time tt, assuming no external source. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
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problems.proof.prevStepproblems.proof.nextStep
U0=Q022C,U(t)=Q(t)22C,Qheat=U0−U(t)=Q022C(1−e−2t/(RC))\boxed{U_0=\frac{Q_0^2}{2C},\quad U(t)=\frac{Q(t)^2}{2C},\quad Q_{\rm heat}=U_0-U(t)=\frac{Q_0^2}{2C}(1-e^{-2t/(RC)})}
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Apply the model consistently to each part, then check dimensions and physical limits.