Question

If $R$ and $L$ denote resistance and inductance respectively which of the following has dimension of time?

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

Answer 1

The correct option is B $\frac{L}{R}$

The time constant of a series LR circuit is given as $\frac{L}{R}$.

The time constant of inductance is :

$\left[L\right]=\left[M{L}^2{T}^{-2}{A}^{-2}\right]$

On the other hand, the dimension of resistance is:

$\left[R\right]=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$

Time constant has the dimension the same as that of time

Time constant $=\frac{L}{R}=\frac{\left[M{L}^2{T}^{-2}{A}^{-2}\right]}{\left[M{L}^2{T}^{-3}{A}^{-2}\right]}$

So, option $B$ has the dimension of time.