Summary

This chapter built up WBCHSE Unit 2's account of current electricity in the order the syllabus lists it. It began with the microscopic picture of a current (Sections 3.2-3.4): free electrons in a metal move randomly and carry no net current until an applied field superimposes a slow drift velocity on this random motion, and this drift velocity, together with the free-electron density and the conductor's cross-section, was shown to give exactly the measured current, $I=nAev_d$, with mobility $\mu=v_d/E$ describing how readily the carriers drift.

It then turned to the macroscopic description of this same behaviour (Sections 3.5-3.7): Ohm's law, $V=IR$, and the material properties resistivity and conductivity that make $R=\rho l/A$ a statement about the material alone, independent of the particular wire's size; the $V$-$I$ characteristic as the direct experimental test of whether a device is ohmic (straight line through the origin) or not (a diode's sharply asymmetric curve being the standard counter-example); and how resistance changes with temperature, rising for a metal (as collisions increase and the relaxation time falls) but falling for a semiconductor (as the number of free carriers rises faster still).

Section 3.8 then showed how resistors combine, in series (adding resistances, splitting voltage) and in parallel (adding conductances, splitting current), with any more elaborate network reduced step by step from these two basic rules. Sections 3.9-3.10 turned to a real cell's own EMF and internal resistance, the terminal PD it actually delivers once current is drawn, and how cells combine in series, in parallel, and in the more general case of unequal EMFs -- both $n$ unequal cells in series and two unequal cells in parallel derived carefully from first principles, rather than merely quoted. …