Question

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

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

Answer 1

The correct option is D

$\left[M{L}^2{T}^{-3}{I}^{-2}\right]$

Step1: Given data.

Mass$=M$

Length$=L$

Time$=T$

Current$=I$

Step2: Find the dimension equation of resistance in an electrical circuit.

We know that,

Formula used:

$R=\frac{V}{I}$

Where $R$ is the resistance of the circuit, $V$ is the voltage, and $I$ is the current.

And,

Voltage, $V=\frac{Workdone\left(W\right)}{Charge\left(q\right)}$

Now,

$R=\frac{{\displaystyle \raisebox{1ex}{$W$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}}{I}$ $\left[\because V=\frac{W}{q}\right]$

$R=\frac{{\displaystyle W}}{q\times I}$

Therefore the dimensional equation of the resistance.

$\left[R\right]=\frac{{\displaystyle \left[M{L}^2{T}^{-2}\right]}}{\left[IT\right]\left[I\right]}$ $\left[\because W=M{L}^2{T}^{-2}andq=IT\right]$

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

Hence, option D is correct.