Question

A standard cell whose e.m.f. is ε₁, a potentiometer whose resistance is 10Ω, an accumulator whose e.m.f., ε₂ is unknown, and a galvanometer G are connected in a circuit, as shown in Fig. At which position of the potentiometer arm will the current through the galvanometer be zero? Find the e.m.f. of the accumulator if the current through the galvanometer is zero when the resistance of the potentiometer segment AB is 9Ω. In this position the cell ε₁ gives a potential drop V₀ across the potentiometer of 2V.

Answer 1

Answer: ε₂ = 1.8V.

Explanation:

The e.m.f. of the standard cell and of the accumulator give currents in opposite directions through the galvanometer. It is clear that the current ceases to flow in the galvanometer circuit when the difference of potential V across the ends of segment AB due to the standard cell is equal to the e.m.f. of the accumulator, i.e.,

V = ε₂.

Since, in the case of a balanced circuit, there is no current in the galvanometer branch, it may be assumed that the potentials f the individual points of the potentiometer increase proportionally to the increase in the resistance of segment AB. i.e.,