An inductor (L = 0.03 H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15V EMF in a circuit shown below. The key K1 has been kept closed for a long time. Then at t = 0, K1 is opened and key K2 is closed simultaneously. At t = 1 ms, the current in the circuit will be : (e5≅150)]

Engineering

Physics

LR Circuit Growth and Decay of Current

Question

An inductor (L = 0.03 H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15V EMF in a circuit shown below. The key K₁ has been kept closed for a long time. Then at t = 0, K₁ is opened and key K₂ is closed simultaneously. At t = 1 ms, the current in the circuit will be : (e⁵≅150)]

6.7 mA

0.67 mA

100 mA

67 mA

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$\frac{15}{0 .15 \times 10^{3}} = 0 .1 A$

$i = i_{0} e^{- \frac{tR}{L}}$

$= 0 .1 e \frac{- 1 \times 10^{- 3} \times 150 \times 100}{. 03}$

$= 0 .1 e^{- 5} \frac{0 .1}{e^{5}} = \frac{0 .1}{150}$