Question

The time constant of $L-R$ circuit is

• A. $LR$
• B. $\frac{L}{R}$
• C. $\frac{R}{L}$
• D. $\frac{1}{LR}$

Answer 1

Answer: (B)

The instantaneous current in $L-R$ circuit during growth is given by
$I=I_0\left(1-e^{-\frac{R_t}{L}}\right)$
Since, all the exponential terms are dimensionless,
therefore, it follows that factor $\frac{R}{L}t$ should be dimensionless i.e.
$\frac{R}{L}t=\left[M^0{L}^0{T}^0\right]$
$\Rightarrow \frac{R}{L}=\frac{\left[M^0{L}^0{T}^0\right]}{[T]}=\left[T^{-1}\right]$
$\Rightarrow \left[\frac{L}{R}\right]=[T]$
Hence, the time constant of $L-R$ circuit is $\left[\frac{L}{R}\right]$.