Question

Dimension of electrical resistance is

• A. $[M{L}^2{T}^{-3}{A}^{-1}]$
• B. $[M{L}^2{T}^{-3}{A}^{-2}]$
• C. $[M{L}^3{T}^{-3}{A}^{-2}]$
• D. $[M{L}^{-1}{L}^3{T}^3{A}^2]$

Answer 1

Answer: (B)

From ohm's law $V=IR$ where $V$ is voltage, $R$ is resistance and $I$ is current.
$\therefore R=\frac{V}{I}$
Dimensions of $R=\frac{\text{ Dimensions of }V}{\text{ Dimensions of }I}$
$=\frac{\left[M{L}^2{T}^{-3}{A}^{-1}\right]}{[A]}$
$=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
Alternative : From definition of time constant $t=RC$, where $R$ is resistance $C$ is capacitance.
$\therefore R=\frac{t}{C}=\frac{[T]}{\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]}$
$R=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$