If L and R are respectively the inductance an | vedclass

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(C) The dimension of inductance $L$ is given by the formula $E = \frac{1}{2} L i^2$,where $E$ is energy and $i$ is current. Thus,$L = \frac{2E}{i^2}$.

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$M^0 L^0 T$

Vedclass · Answer

(C) The dimension of inductance $L$ is given by the formula $E = \frac{1}{2} L i^2$,where $E$ is energy and $i$ is current. Thus,$L = \frac{2E}{i^2}$.Substituting dimensions: $[L] = \frac{[ML^2T^{-2}]}{[A^2]} = [ML^2T^{-2}A^{-2}]$.The dimension of resistance $R$ is given by $V = iR$,so $R = \frac{V}{i} = \frac{W}{qi} = \frac{W}{i^2t}$.Substituting dimensions: $[R] = \frac{[ML^2T^{-2}]}{[A^2T]} = [ML^2T^{-3}A^{-2}]$.Now,the dimension of $\frac{L}{R}$ is $\frac{[ML^2T^{-2}A^{-2}]}{[ML^2T^{-3}A^{-2}]} = [T]$.Therefore,the dimensions of $\frac{L}{R}$ are $[M^0 L^0 T^1]$.

If $L$ and $R$ are respectively the inductance and resistance,then the dimensions of $\frac{L}{R}$ will be

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