Introduction

The Carey Foster bridge is an electrical circuit that can be used to measure very small resistances. It works on the same principle as Wheatstone’s bridge, which consists of four resistances, P, Q, R and S that are connected to each other as shown in the circuit diagram in Figure 1. In this circuit, G is a galvanometer, E is a lead accumulator, and K1 and K are the galvanometer key and the battery key respectively. If the values of the resistances are adjusted so that no current flows through the galvanometer, then if any three of the resistances P, Q, R and S are known, the fourth unknown resistance can be determined by using the relationship P R = Q S (1)

Figure 1: Wheatstone’s bridge You may be familiar with the post office box and the meter bridge, which also work on the same principle as Wheatstone’s bridge. In the meter bridge, two of the resistors, R and S, say, are replaced by a one meter length of resistance wire, with uniform cross-sectional area fixed on a meter scale. Point D is an electrical contact that can be moved along the

wire, thus varying the magnitudes of resistances R and S. The Carey Foster bridge is a modified form of the meter bridge in which the effective length of the wire is considerably increased by connecting a resistance in series with each end of the wire. This increases the accuracy of the bridge. While performing this experiment you will balance the Carey Foster bridge by a null deflection method using a galvanometer. You will first determine the resistance per unit length of the material used for the bridge wire, and will then determine the value of an unknown resistance.

Apparatus

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Carey Foster bridge two equal resistances of about 2 ohms each thick copper strip fractional resistance box lead accumulator galvanometer unknown low resistance one way key connecting wires

lead accumulator

fractional resistance box

standard resistances

bridge wire

galvanometer

Figure 2: Experimental setup for the Carey Foster bridge.

Theory

The aim of the experiment is to determine the resistance per unit length, ρ of the Carey Foster bridge wire and hence to find the resistance of a given wire of low resistance. The experimental setup is shown in Figure 2, and a circuit diagram for the experiment is shown in Figure 3. There are four gaps in this arrangement. The standard low resistances, P and Q, of 2 Ω each are connected in the inner gaps 2 and 3. The known resistance, i.e., the fractional resistance box X and the unknown resistance Y whose resistance is to be determined are connected in the outer gaps 1 and 4, respectively. A one meter long resistance wire EF of uniform area of cross section is soldered to the ends of two copper strips. Since the wire has uniform cross-sectional area, the resistance per unit length is the same along the wire. A galvanometer G is connected between terminal B and the jockey D, which is a knife edge contact that can be moved along the meter wire EF and pressed to make electrical contact with the wire. A lead accumulator with a key K in series is connected between terminals A and C.

Figure 3: Circuit diagram for the Carey Foster bridge The position of jockey D is adjusted to locate the position where there is no deflection of the galvanometer when the jockey is pressed to make electrical contact with the wire; this position is called the balance point or null point. The bridge has its highest sensitivity when all four of the resistances, P, Q, X and Y, have similar magnitudes. The four points A, B, C and D in Figure 3 exactly correspond to the points labeled A, B, C and D in the circuit diagram of Wheatstone’s bridge in Figure 1, and thus the Carey Foster Bridge effectively works like a Wheatstone’s bridge. If the balance point is located at a distance l1 from E, then we can write the condition of balance as ( X + α + l1 ρ ) P R = = , (2) Q S {Y + β + (100 − l1 )ρ }

where α and β are...