Question

The dimensional formula of time constant ${}^{\prime }L/R^{\prime }$ during growth and decay of current in an inductive circuit is same as that of

• A. time
• B. current
• C. constant
• D. resistance

Answer 1

Answer: (A)

Growth of current in $LR$ circuit
$I=\frac{\epsilon }{R}\left[1-e^{-\frac{Rt}{L}}\right]$
Decay of current in $LR$ circuit $I=\frac{\epsilon }{R}{e}^{-\frac{Rt}{L}}$
In physics, the powers are dimensionless
$\Rightarrow \left[\frac{Rt}{L}\right]=$ dimensionless, or $[t]=\left[\frac{L}{R}\right]$