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Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
A
$ML^2T^{-2}$
B
$ML^2T^{-1}I^{-1}$
C
$ML^2T^{-3}I^{-2}$
D
$ML^2T^{-3}I^{-1}$
Detailed Solution
Resistance: $R = \dfrac{V}{I}$
Potential difference $V = \dfrac{\text{work}}{\text{charge}} = \dfrac{[ML^2T^{-2}]}{[IT]} = [ML^2T^{-3}I^{-1}]$
$[R] = \dfrac{[V]}{[I]} = \dfrac{[ML^2T^{-3}I^{-1}]}{[I]}$
$[R] = [ML^2T^{-3}I^{-2}]$
Check using power: $P = I^2R \Rightarrow [R] = \dfrac{[ML^2T^{-3}]}{[I^2]} = [ML^2T^{-3}I^{-2}]$
Potential difference $V = \dfrac{\text{work}}{\text{charge}} = \dfrac{[ML^2T^{-2}]}{[IT]} = [ML^2T^{-3}I^{-1}]$
$[R] = \dfrac{[V]}{[I]} = \dfrac{[ML^2T^{-3}I^{-1}]}{[I]}$
$[R] = [ML^2T^{-3}I^{-2}]$
Check using power: $P = I^2R \Rightarrow [R] = \dfrac{[ML^2T^{-3}]}{[I^2]} = [ML^2T^{-3}I^{-2}]$