Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, length $L$, time $T$, an

Question

Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, length $L$, time $T$, and current $I$, would be:

Accepted Answer

1. **Identify the formula for Resistance:** According to Ohm's law, Resistance ($R$) is given by the ratio of potential difference ($V$) to current ($I$): $R = \frac{V}{I}$.
2. **Find the dimensions of Potential Difference ($V$):** Potential difference is defined as work done per unit charge, $V = \frac{W}{Q}$.
   - The dimensional formula for Work ($W$) is $[M L^2 T^{-2}]$.
   - The dimensional formula for Charge ($Q = I 	imes t$) is $[I T]$.
   - Therefore, the dimensions of $V = \frac{[M L^2 T^{-2}]}{[I T]} = [M L^2 T^{-3} I^{-1}]$.
3. **Calculate the dimensions of Resistance ($R$):** Substitute the dimensional formula of $V$ and $I$ back into the resistance equation:
   $R = \frac{[M L^2 T^{-3} I^{-1}]}{[I]} = [M L^2 T^{-3} I^{-2}]$.

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