Find the equation for the current $i$ in a series circuit with inductance $L=0.1 \mathrm{H}$, resistance $R=8$ ohms, and voltage $\mathrm{V}=12$ volts. The initial current $\mathrm{i} 0=2$ amperes when $\mathrm{t}=0$.
A) $i=0.5 e^{-80 t}+1.5$ amperes
B) $\mathrm{i}=0.5 \mathrm{e}^{-80 \mathrm{t}}-1.5$ amperes
C) $i=2 e^{-80 t}+1.5$ amperes
D) $i=2 e^{-80 t}-1.5$ amperes

Question

Quizplus · Accepted Answer

The equation for the current in an RL circuit is $i(t) = i_0 e^{-\frac{R}{L}t} + \frac{V}{R}(1 - e^{-\frac{R}{L}t})$. Substituting the given values, $i(t) = 2 e^{-80t} + \frac{12}{8}(1 - e^{-80t}) = 0.5 e^{-80t} + 1.5$.

Find the Equation for the Current iii In a Series Circuit with Inductance

Find the Equation for the Current $i$ In a Series Circuit with Inductance