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)

$\frac{L}{R}$

The instantaneous current in L-R circuit during growth is given by

$I=I_0(1-e^{-\frac{R}{L}t})$

Since, all the exponential terms are dimesionless, therefore, it follows that factor $\frac{R}{L}t$ should be dimensionless i.e.

$\frac{R}{L}t=\left[M^0{L}^0{T}^0\right]$

$\Rightarrow \frac{R}{L}=\frac{\left[M^0{L}^0{T}^0\right]}{\left[T\right]}=\left[T^{-1}\right]$

$\Rightarrow \left[\frac{L}{R}\right]=\left[T\right]$

Hence, the time constant of L-R circuit is $\left[\frac{L}{R}\right]$.