Question

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) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]\)
(b) \(\left[M L^{2} T^{-1} I^{-1}\right]\)
(c) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{l}^{-2}\right]\)(d) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{l}^{-1}\right]\)

Answer 1

Correct Option (c) \(\left[M L^{2} T^{-3} \mathrm{Y}^{-2}\right]\)
Explanation:
According to Ohm's law
$$
\begin{gathered}
V=R I \text { or } \quad R=\frac{V}{I} \\
\text { Dimensions of } V=\frac{W}{q}=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{IT}]} \\
\therefore \quad R=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} / \mathrm{IT}\right]}{[\mathrm{I}]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{l}^{-2}\right] .
\end{gathered}
$$