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Electric Current

Problem 3.204

The electrodes of a capacitor of capacitance \(C=2.00 \mu \mathrm{F}\) carry opposite charges \(q_{0}=1.00 \mathrm{mC} .\) Then the electrodes are interconnected through a resistance \(R=5.0 \mathrm{M\Omega.}\) Find: (a) the charge flowing through that resistance during a time interval \(\tau=2.00 \mathrm{~s}\) (b) the amount of heat generated in the resistance during the same interval.

Reveal Answer
3.204.(a)q=q0(1−e−τ/RC)=0.18mC; (b) Q==(1−e−2τ/RC)q02/2C=82 mJ\begin{aligned} & & 3.204 .(a) & q=q_{0}\left(1-e^{-\tau / R C}\right)=0.18 \mathrm{mC} ; & \text { (b) } Q=\\ =&\left(1-\mathrm{e}^{-2 \tau / R C}\right) q_{0}^{2} / 2 C &=82 \mathrm{~mJ} \end{aligned}
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