Question
What fraction of the initial current still flows in the circuit of Fig. 34-1 seven time constants after the switch has been closed?
Step 1
Step 1: Recall that when a switch is closed in an RC circuit, the current decays exponentially according to the equation: I(t) = Iâ‚€e^(-t/Ď„) where Iâ‚€ is the initial current, t is the time elapsed, and Ď„ is the time constant. Show more…
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By what fraction does the current in Fig. 34-2 differ from $i_{\infty}$ three time constants after the switch is first closed?
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If, in Fig. $34-2, R=20 \Omega, L=0.30 \mathrm{H}$, and $\mathscr{E}=90 \mathrm{~V}$, what will be the current in the circuit $0.050 \mathrm{~s}$ after the switch is closed? We are going to use the exponential equation for $i$ given on p. 374 . The time constant for this circuit is $L / R=0.015 \mathrm{~s}$, and $i_{\infty}=\mathscr{/} R=4.5 \mathrm{~A}$. Then $$ i=i_{\infty}\left(1-e^{-t / L / R}\right)=(4.5 \mathrm{~A})\left(1-e^{-3.33}\right)=(4.5 \mathrm{~A})(1-0.0357)=4.3 \mathrm{~A} $$
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