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Q.

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]

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a

$R = VI$

b

$R = \sqrt{P I}$

c

$R = \frac{E}{I^{2} t}$

d

$R = VP$

answer is B.

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Detailed Solution

$Dimensional formula of power = \frac{W}{t} = \frac{{ML}^{2} T^{- 2}}{T} = [{ML}^{2} T^{- 3}] Current \to [A] V = \frac{W}{q} = \frac{{ML}^{2} T^{- 2}}{AT} = [{ML}^{2} T^{- 3} A^{- 1}] E = [{Ml}^{2} T^{- 2}] S_{o}, R = \frac{E}{I^{2} t} = \frac{{ML}^{2} T^{- 2}}{A^{2} T} \Rightarrow [{ML}^{2} T^{- 3} A^{- 2}] and V = IR \Rightarrow R = \frac{{ML}^{2} T^{- 3} A^{- 2}}{A} \Rightarrow [{ML}^{2} T^{- 3} A^{- 2}]$

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