First slide

Time -Varying current in L-R circuit

Question

Switch s of the circuit, shown in figure, is closed at t = 0. If e denotes the induced emf in L and i, the current flowing through the circuit at time t, which of the following graphs is correct?

Moderate

A
B
C
D

Solution

At the time t = 0, e is max and is equal to E, but current i is zero.
$A t t i m e t, i = \frac{E}{R} (1 - e^{- \frac{R t}{L}}) T h e r e f o r e e = L \frac{d i}{d t} = \frac{E}{L} e^{- R t / L} . S o e d e c r e a s e s e x p o n e n t i a l l y .$

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