Question

What is the dimensional formula of electric potential?

• A. \( [L^{2}T^{-3}A^{-1}] \)
• B. \( [L^{2}T^{-2}A^{-1}] \)
• C. \( [ML^{2}T^{-3}A^{-2}] \)
• D. \( [L^{2}T^{-2}A^{-2}] \)

Hint:

Remember the important dimensional formulas: \[ \begin{aligned} \text{Work} &=[ML^{2}T^{-2}],\\ \text{Charge} &=[AT],\\ \text{Potential} &=\frac{\text{Work}}{\text{Charge}} =[ML^{2}T^{-3}A^{-1}],\\ \text{Resistance} &=\frac{\text{Potential}}{\text{Current}} =[ML^{2}T^{-3}A^{-2}]. \end{aligned} \] Always derive the dimensions from the defining formula instead of memorizing them separately.

Answer 1

The Correct Option is C

Electric potential is defined as $V = W/q$, where $W$ is work done and $q$ is charge. With $[W] = ML^2T^{-2}$ and $[q] = AT$, substituting gives $[V] = ML^2T^{-2}/(AT) = ML^2T^{-3}A^{-1}$.