Question
In Fig. $34-2, R=5.0 \Omega, L=0.40 \mathrm{H}$, and $\varepsilon=20 \mathrm{~V}$. Find the current in the circuit $0.20 \mathrm{~s}$ after the switch is first closed.
Step 1
Here, $L = 0.40 \, \text{H}$ and $R = 5.0 \, \Omega$. So, we substitute these values into the formula to get: \[\tau = \frac{0.40 \, \text{H}}{5.0 \, \Omega} = 0.08 \, \text{s}\] Show more…
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If, in Fig. 34-2, $R=20 \Omega$, $L=0.30 \mathrm{H}$, and $\varepsilon=90 \mathrm{~V}$, 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 in Eq. (34.9). The time constant for this circuit is $\mathrm{L} / \mathrm{R}=0.015 \mathrm{~s}$, and $i_{\infty}=\varepsilon / \mathrm{R}=$ $4.5 \mathrm{~A}$. Then $$ i=i_{x}\left(1-e^{-i /\langle L / R)}\right)=(4.5 \mathrm{~A})\left(1-e^{-333}\right)=(4.5 \mathrm{~A})(1-0.0357)=4.3 \mathrm{~A} $$
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 $$ i=i_{\infty}\left(1-e^{-t / L / R}\right)=(4.5 \mathrm{~A})\left(1-e^{-3.33}\right)=(4.5 \mathrm{~A})(1-0.0357)=4.3 \mathrm{~A} $$
. In Fig. $30.11 .$ suppose that $\varepsilon=60.0 \mathrm{~V}, R=240 \Omega .$ and $L=0.160 \mathrm{H}$. With switch $S_{2}$ open, switch $S_{1}$ is left closed until a constant currcnt is cstablishcd. Then $S_{2}$ is closcd and $S_{1}$ opcned, taking the battery out of the circuit. (a) What is the initial current in the resistor, just after $S_{2}$ is closed and $S_{1}$ is opened? (b) What is the current in the resistor at $t=4.00 \times 10^{-4} \mathrm{~s} ?$ (c) What is the potcntial differcnoe betwecn points $b$ and $c$ at $t=4.00 \times 10^{-4} \mathrm{~s}$ ? Which point is at a higher potcntial? (d) How long does it take the current to decrease to half its initial value?
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