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

Answer 1

The Correct Option is C

To determine the dimensional formula of resistance in an electrical circuit, we start with the Ohm's Law, which states:

V = IR

where:

• V is the voltage with dimensional formula [ML^2T^{-3}I^{-1}]
• I is the current with dimensional formula [I]
• R is the resistance (unknown)

The dimensional formula for resistance can be derived by rearranging Ohm's law:

R = \frac{V}{I}

Substituting the dimensional formulas, we have:

[R] = \frac{[ML^2T^{-3}I^{-1}]}{[I]}

This simplifies to:

[R] = [ML^2T^{-3}I^{-2}]

Thus, the correct dimensional formula of resistance is [ML^2T^{-3}I^{-2}].

Conclusion: The correct answer is [ML^2T^{-3}I^{-2}], which corresponds to the given correct option.