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.
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Collect results in the order asked. Dimensions and physical signs provide independent checks; they do not replace the derivation but can expose algebraic errors.