First slide

Time -Varying current in L-R circuit

Question

In the network shown, switch s is closed at t=0. Then which of the following graphs correctly shown the variation of induced emf between points ‘a’ and ‘b’?

Moderate

A
B
C
D

Solution

$\begin{array}{l} i = \frac{E}{R} (1 - e^{- \frac{R t}{L}}) \Rightarrow \frac{di}{dt} = \frac{E}{L} e^{- \frac{R t}{L}} \\ ∴ V_{ab} = L \frac{di}{dt} = {Ee}^{- \frac{R t}{L}} \end{array}$

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