Current Electricity — MHT-CET Physics

A cell's e.m.f. is the voltage it would show with no current; drawing a current I through its internal resistance r lowers the terminal voltage to E − Ir, cells in series add their e.m.f.s and internal resistances, and identical cells in parallel keep their e.m.f. but share the current.

At any junction the current flowing in equals the current flowing out (Kirchhoff's first law, conservation of charge), and round any closed loop the e.m.f.s add up to the voltage drops (the second law, conservation of energy); between them they solve any network of cells and resistors.

A Wheatstone bridge of four resistances P, Q, R and S is balanced, with no current in the galvanometer, when P/Q = R/S; the metre bridge is the same bridge with R and S replaced by the two lengths of a uniform wire, so an unknown resistance is read as X/R = l/(100 − l).

A steady current through a long uniform wire gives a constant potential drop per unit length, the potential gradient k; a cell connected against the wire balances at the length where kl equals its e.m.f., drawing no current, so the potentiometer measures e.m.f. directly and compares two cells by their balancing lengths.

A galvanometer of resistance G gives full-scale deflection at a small current I_g; a small shunt S in parallel lets it measure a larger current I as an ammeter, with I_g G = (I − I_g)S, and a large resistance in series lets it read a voltage V as a voltmeter, with V = I_g(G + R).