Problem 2
A uniform wire of length L and constant cross-sectional area A has resistivity ρ at fixed temperature. Its ends are connected to an ideal constant-voltage source V; take ρ unchanged by heating, with steady current and no leakage. (a) Find wire resistance R from resistivity. (b) Calculate current I and current density J. (c) Find Joule power P and describe its dependence on L when V,A,ρ are fixed. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
problems.proof.stepOf
problems.proof.analysis
The equation follows by applying the physical law to the chosen system; ideal constraints link the variables. Signs must remain consistent with the defined directions.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.