A series circuit consists of an open switch, an ideal emf source $\varepsilon _ { 0 }$, a $5.0 - \mathrm { k } \Omega$ resistor, and a 4.0-H inductor. If the potential across the resistor is $65.0 \mathrm {~V}$ at $2.0 \mathrm {~ms}$ after the switch is closed, find the source emf, $\varepsilon _ { 0 }$.
A) $56 \mathrm {~V}$
B) $36 \mathrm {~V}$
C) $76 \mathrm {~V}$
D) $71 \mathrm {~V}$

Question

Quizplus · Accepted Answer

The voltage across the resistor in an RL circuit is given by $ V_R = \varepsilon_0 (1 - e^{-t/\tau}) $, where $\tau = L/R$. Solving for $\varepsilon_0$ using $ V_R = 65 \mathrm{~V} $, $ R = 5000 \mathrm{~\Omega} $, $ L = 4.0 \mathrm{~H} $, and $ t = 2.0 \mathrm{~ms} $, we find $\varepsilon_0 \approx 71 \mathrm{~V}$.

A Series Circuit Consists of an Open Switch, an Ideal ε0\varepsilon _ { 0 }ε0​

A Series Circuit Consists of an Open Switch, an Ideal $\varepsilon _ { 0 }$