Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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

$[M L^2 T^{-3} I^{-1}]$

$[M L^2 T^{-2}]$

$[M L^2 T^{-1} I^{-1}]$

$[M L^2 T^{-3} I^{-2}]$

Identify the formula for Resistance: According to Ohm's law, Resistance ( $R$ ) is given by the ratio of potential difference ( $V$ ) to current ( $I$ ): $R = \frac{V}{I}$ .
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 ( $Q = I \times t$ ) is $[I T]$ .
Therefore, the dimensions of $V = \frac{[M L^2 T^{-2}]}{[I T]} = [M L^2 T^{-3} I^{-1}]$ .

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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