Question

Dimension of electrical resistance is

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

Answer 1

Answer: (B)

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