The dimensional formula of j omega L is . . | vedclass

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Question

(A) The term $j \omega L$ represents inductive reactance $(X_L)$,which has the same dimensions as resistance $(R)$.Resistance is defined as $R = \frac

Vedclass · Accepted Answer

$M^{1} L^{2} T^{-1} Q^{-2}$

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(A) The term $j \omega L$ represents inductive reactance $(X_L)$,which has the same dimensions as resistance $(R)$.Resistance is defined as $R = \frac{V}{I}$.Since $V = \frac{W}{Q}$ (where $W$ is work/energy and $Q$ is charge) and $I = \frac{Q}{t}$ (where $t$ is time),$R = \frac{W/Q}{Q/t} = \frac{W \cdot t}{Q^2}$.The dimensional formula for work $(W)$ is $[M^1 L^2 T^{-2}]$.Substituting the dimensions: $R = \frac{[M^1 L^2 T^{-2}] \cdot [T^1]}{[Q^2]} = [M^1 L^2 T^{-1} Q^{-2}]$.Therefore,the correct option is $A$.

The dimensional formula of $j \omega L$ is . . . . . . . Take $Q$ as the dimension of charge.

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