(a) Derive the base units of resistivity from V = W/Q, Q = It, R = V/I and ρ = RA/L. (b) For displacement s, speed u, acceleration a and time t, test s = ut + at and s = ut + 3at² for homogeneity. Can the test establish the correct numerical coefficient?

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ρ: kg m³ s⁻³ A⁻². ut has unit m but at has unit m s⁻¹, so the first equation fails. Both terms in the second have unit m, but dimensional analysis cannot validate the coefficient 3. Energy has unit kg m² s⁻² and charge A s, so potential difference has unit kg m² s⁻³ A⁻¹. Divide by A to get resistance; multiply by m²/m to get resistivity. Compare every term: [ut] = m, [at] = m s⁻¹, [at²] = m. Reject the first equation and accept only dimensional consistency of the second. State that homogeneous equations may still be physically false.

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(a) Derive the base units of resistivity from V = W/Q, Q = It, R = V/I and ρ = RA/L. (b) For displacement s, speed u, acceleration a and time t, test s = ut + at and s = ut + 3at² for homogeneity. Can the test establish the correct numerical coefficient?

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