Question

Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, of length $L$, of time $T$ and of current $I$ would be

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

Answer 1

Answer: (D)

According to Ohm’s law
$V=IR$
or $R=\frac{V}{I}$
Dimensions of $V=\frac{W}{q}=\frac{\left[ML^{2}T^{-2}\right]}{\left[IT\right]}$
$\therefore $ Dimensions of $R=\frac{\left[ML^{2}T^{-2}/IT\right]}{I}$
$=\left[ML^{2}T^{-3}I^{-2}\right]$