First slide

Time -Varying current in L-R circuit

Question

An ideal coil of 10 H is joined in series with a resistance of $5 Ω$ and a battery of 5 V. 2 s after joining, the current flowing in ampere in the circuit will be

Moderate

A

$e^{- 1}$
B

$1 - e^{- 1}$
C

$1 - e$
D

e

Solution

From $i = i_{0} [1 - e^{- Rt / L}], where i_{0} = \frac{5}{5} = 1 A$
$∴ i = 1 (1 - e^{\frac{- 5 \times 2}{10}}) = (1 - e^{- 1}) A$

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