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

Answer 1

Answer: (B)

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