Question

The time constant of an $L-R$ circuit is

• A. $LR$
• B. $\frac{L}{R}$
• C. $\frac{R}{L}$
• D. $\frac{L^2}{R}$

Answer 1

Answer: (B)

$\frac{L}{R}$

By definition, potential difference across inductor$=\Delta V=L\frac{dI}{dt}$

Hence in a $L-R$ circuit applying Kirchoff's Voltage Law,

Net potential drop across the circuit$=V-IR-L\frac{dI}{dt}=0$

Integrating the above expression we get, $I=\frac{V}{R}(1-e^{\frac{-Rt}{L}})$

Hence time constant$=\frac{L}{R}$.