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 [ML²T⁻³I⁻¹]
B [ML²T⁻²]
C [ML²T⁻¹I⁻¹]
D [ML²T⁻³I⁻²]

Answer 1

The dimensions of resistance in an electrical circuit are represented by ML²T⁻³I⁻², which corresponds to option D.

Step-by-step explanation:

To find the dimensions of resistance (R) in an electrical circuit, we can use the formula R = ρL/A, where ρ (rho) is the resistivity, L is the length, and A is the cross-sectional area. In terms of the basic SI units, resistivity (ρ) has the dimensions of ohm-meter (Ω·m), which can be broken down into ML³T⁻³I⁻². Using the dimension of resistivity, we can deduce the dimensions of resistance (R) by accounting for the length (L) and cross-sectional area (A), which is length squared (L²), giving us M·L⁻¹·T⁻³·I⁻². Since the length (L) is in the numerator for the formula of resistance, this cancels out one of the L's from ρ, resulting in ML²T⁻³I⁻² as the correct dimensional formula for resistance.

Therefore, the correct answer to the student's question would be D [ML²T⁻³I⁻²] as the dimensions of resistance.