For positive constants 
, and 
define the current in a circuit at time 
by
![\[ I(t) = \frac{E}{R} \left( 1 - e^{-\frac{Rt}{L} \right). \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-bd0915a0854c846dcb425bdac8f1ddae_l3.png "Rendered by QuickLaTeX.com")
Determine the value of
![\[ \lim_{R \to 0^+} I(t). \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-95c8ed76d63ee0bf66e7d23c8408e778_l3.png "Rendered by QuickLaTeX.com")
We use L’Hopital’s rule to compute the limit as follows,
![\begin{align*} \lim_{R \to 0^+} I(t) &= \lim_{R \to 0^+} \frac{E - Ee^{-\frac{Rt}{L}}}{R} \\[9pt] &= \lim_{R \to 0^+} \frac{\frac{Et}{L} e^{-\frac{Rt}{L}}}{1} \\[9pt] &= \frac{tE}{L}. \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-0493653e3a789277a23f4c0431d37bc8_l3.png "Rendered by QuickLaTeX.com")
For positive constants , and define the current in a circuit at time by
Determine the value of
We use L’Hopital’s rule to compute the limit as follows,