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. $\left[M{L}^2{T}^{-3}{I}^{-1}\right]$
• B. $\left[M{L}^2{T}^{-2}\right]$
• C. $\left[M{L}^2{T}^{-1}{I}^{-1}\right]$
• D. $\left[M{L}^2{T}^{-3}{I}^{-2}\right]$

Answer 1

Answer: (D)

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

Ohm's law: $R=\frac{V}{I}$

Also, $W=Vq$$⟹V=\frac{W}{q}$ (where, $q=It$)

$⟹$ $R=\frac{W}{qI}=\frac{W}{I^{2}t}$

Dimensions of work done, $W=\left[M{L}^2{T}^{-2}\right]$

$\therefore$ Dimension of resistance, $R=\frac{\left[M{L}^2{T}^{-2}\right]}{I^{2}T}=\left[M{L}^2{T}^{-3}{I}^{-2}\right]$