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# A coil of inductance $L= 150\;mH$ and resistance $R= 70\;m \Omega$ is connected to a voltage source. How soon will the voltage attain $50\%$ of initial value

$(a)\;2.82 \;s \\(b)\;1.49\;s \\ (c)\;2.49\;s \\ (d)\;0.14\;s$

$I= I_{max} [1-e^{\large\frac{-Rt}{L}}]$
$\large\frac{I}{I_{max}}=\frac{1}{2}$ given
$e^{\large\frac{Rt}{L}}=0.5$
$\large\frac{Rt}{L} $$=\log_e2 t= \large\frac{L}{R} \log _e^2 =\large\frac{150 \times 10^{-3}}{70 \times 10^{-3}}$$ \times 0.6931$
$\qquad= 1.495$
Hence b is the correct answer.