The resistance R of a certain metal wire varies with its temperature according to R=R0(1+αΔT), where R0 is the resistance at the reference temperature, ΔT=T−T0 and α is the temperature coefficient of resistance.
(i) When a constant potential difference V is applied across the wire, derive an expression for the current I in terms of R0, α and ΔT.
(ii) Show algebraically that, as the wire heats up, the plot of V (vertical axis) against I (horizontal axis) will not be a straight line.
(iii) Given R0=4Ω, α=0.004∘C−1 and V=8V, calculate the current when ΔT=0∘C and when ΔT=100∘C.
(iv) Using your numerical results, comment on how the slope of the V–I curve changes with temperature.