Question

Dimensional formula of the physical quantity, resistance is

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

Answer 1

Answer: (A)

According to Ohm's law,
$V=IR$
$\therefore \, R=\frac{V}{I}$
But $V=\frac{W}{q}$
$=\frac{W}{I t}$ $\left[\because q = I t\right]$
$\therefore R=\frac{W / I t}{I}$
$=\frac{W}{I^{2} t}$
Hence, $\left[R\right]=\frac{\left[W\right]}{\left[I^{2}\right] \left[t\right]}=\frac{\left[M L^{2} T^{- 2}\right]}{\left[A^{2} T\right]}$
$=\left[M L^{2} T^{- 3} A^{- 2}\right]$