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 next part uses the preceding result as input rather than treating parts independently. This keeps conventions and physical state consistent throughout.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.