Question

What is the dimensional formula of resistance?

• A. $\left[M^{-1}{L}^{-2}{T}^4{A}^{-2}\right]$
• B. $\left[M^{}{L}^2{T}^{-5}{A}^{-3}\right]$
• C. $\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$
• D. None of these

Answer 1

The correct option is D None of these

By ohm's law, ratio of V and I is constant equal to resistance $R$. Hence,

$V=IR$, $R=\frac{V}{I}$.

$\left[R\right]=\frac{\left[V\right]}{\left[I\right]}=\frac{\left[M{L}^2{A}^{-1}{T}^{-3}\right]}{\left[A\right]}=\left[M{L}^2{A}^{-2}{T}^{-3}\right]$