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(A) The time constant of an $LR$ circuit is given by $	au = \frac{L}{R}$.Dimensional formula of inductance $L$ is $[M^{1} L^{2} T^{-2} A^{-2}]$.Dimen

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$[L^{0} M^{0} T^{1}]$

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(A) The time constant of an $LR$ circuit is given by $	au = \frac{L}{R}$.Dimensional formula of inductance $L$ is $[M^{1} L^{2} T^{-2} A^{-2}]$.Dimensional formula of resistance $R$ is $[M^{1} L^{2} T^{-3} A^{-2}]$.Therefore,the dimensions of $\frac{L}{R}$ are:$\frac{[M^{1} L^{2} T^{-2} A^{-2}]}{[M^{1} L^{2} T^{-3} A^{-2}]} = M^{1-1} L^{2-2} T^{-2-(-3)} A^{-2-(-2)} = M^{0} L^{0} T^{1} A^{0}$.Thus,the dimensions of $\left(\frac{L}{R}ight)$ are $[L^{0} M^{0} T^{1}]$.

Let the inductance and resistance be denoted by $L$ and $R$ respectively. The dimensions of $\left(\frac{L}{R}\right)$ are

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