Kirchhoff's junction (current) law states that the algebraic sum of currents meeting at a junction is zero, that is, the total current entering a junction equals the total current leaving it; it is based on conservation of charge. Kirchhoff's loop (voltage) law states that the algebraic sum of the changes in potential around any closed loop of a circuit is zero; it is based on conservation of energy.

sum(I) at junction = 0; sum(V) around loop = 0

A Wheatstone bridge has four resistances P, Q, R and S arranged in a quadrilateral, with a galvanometer between the junctions of P-Q and R-S, and a cell across the other diagonal. When the bridge is balanced, no current flows through the galvanometer, so the junction connected by the galvanometer are at the same potential. Applying Kirchhoff's laws, the potential drops give P/Q = R/S. This is the balance condition; if three resistances are known, the fourth can be found.

P/Q = R/S

Given emf E = 2 V, internal resistance r = 0.5 ohm, external resistance R = 4.5 ohm. Current I = E/(R + r) = 2/(4.5 + 0.5) = 2/5 = 0.4 A. Terminal potential difference V = I R = 0.4 x 4.5 = 1.8 V (equivalently V = E - I r = 2 - 0.4 x 0.5 = 1.8 V).

I = E/(R + r); V = E - I r