GATE ECE 2009 | Question: 30

Question

The time domain behavior of an $R L$ circuit is represented by
\[ L \frac{d i}{d t}+R i=V_{o}\left(1+B e^{-R t / L} \sin t\right) u(t). \]
For an initial current of $i(0)=\dfrac{V_{o}}{R}$, the steady state value of the current is given by

• A. $ i(t) \rightarrow \frac{V_{0}}{R}$
• B. $ i(t) \rightarrow \frac{2 V_{0}}{R}$
• C. $ i(t) \rightarrow \frac{V_{0}}{R}(1+B)$
• D. $ i(t) \rightarrow \frac{2 V_{0}}{R}(1+B)$