Question

The dimensionally correct expression for the resistance $R$ among the following is $[P=$ electric power, $I=$ electric current, $t=$ time, $V=$ voltage and $E=$ electric energy]

• A. $R=\sqrt{PI}$
• B. $R=\frac{E}{I^{2}t}$
• C. $R=V^{2}P$
• D. $R=VI$

Answer 1

Answer: (B)

Dimensional formula of power
$=\frac{W}{t}=\frac{M{L}^2{T}^{-2}}{T}=\left[M{L}^2{T}^{-3}\right]$ Current $\to [A]$
$V=\frac{W}{q}=\frac{M{L}^2{T}^{-2}}{AT}=\left[M{L}^2{T}^{-3}{A}^{-1}\right]$
$E=\left[M{L}^2{T}^{-2}\right]$
So, $R=\frac{E}{l^{2}t}=\frac{M{L}^2{T}^{-2}}{A^{2}T}$
$\Rightarrow \left[M{L}^{2}T-3A^{-2}\right]$
and $V=IR\Rightarrow R=\frac{M{L}^2{T}^{-3}{A}^{-1}}{A}$
$\Rightarrow \left[M{L}^{2}T-3A^{-2}\right]$
So, (2) is the correct formula.