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An ideal inductor $L$ and resistor $R$ are connected in series across a DC source of EMF $\varepsilon$. The time constant of the circuit and the steady-state current are:
A$\tau = RL,\quad I_\infty = \varepsilon/R$
B$\tau = R/L,\quad I_\infty = \varepsilon L/R$
C$\tau = L/R,\quad I_\infty = \varepsilon L$
D$\tau = L/R,\quad I_\infty = \varepsilon/R$
Answer & Solution
Correct answer: D. $\tau = L/R,\quad I_\infty = \varepsilon/R$
Solving $L\dfrac{di}{dt} + Ri = \varepsilon$ gives $i(t) = (\varepsilon/R)\left[1 - e^{-Rt/L}\right]$. The time constant is $\tau = L/R$ (the time to reach $\approx 63\%$ of the final value) and the steady-state current as $t \to \infty$ is $\varepsilon/R$.
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