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 ire, 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 • • • • • • • • •

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, ? 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 ? 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 + ? + l1 ? ) P R = = , (2) Q S {Y + ? + (100 ? l1 )? } where ? and ? are the end corrections at the left and right ends.

These end corrections include the resistances of the metal strips to which the wire is soldered, the contact resistances between the wire and the strips, and they also allow for the non-coincidence of the ends of the wire with the zero and one hundred division marks on the scale. If the positions of X and Y are interchanged, i. e. , X is put in gap 4 and Y in gap 1, and the balance point is found at a distance l2 from E, then the balance condition becomes (Y + ? + l 2 ? ) P R = = (3) Q S {X + ? + (100 ? l 2 )? } Combining Equations 2 and 3, we obtain ( X + ? l1 ? ) (Y + ? + l 2 ? ) (4) = {Y + ? + (100 ? l1 )? } {X + ? + (100 ? l 2 )? } Adding 1 on both sides and simplifying, ( X + ? + Y + ? + 100 ? ) (Y + ? + X + ? + 100 ? ) = (5) {Y + ? + (100 ? l1 ) ? } { X + ? + (100 ? l2 ) ? } Since the numerators are equal, we can write Y + ? + (100 ? l1 )? = X + ? + (100 ? l 2 )? , (6) X ? Y = (l 2 ? l1 )? , (7) Y = X ? (l 2 ? l1 )? (8) This relation shows that the difference between the known and unknown resistance is equal to the resistance of the bridge wire between the two balance points. Once we know l1, l2, ? nd X, the unknown resistance Y can be determined. Clearly balance points will only be possible if the difference between the resistances, X – Y, is less than the total resistance of the one meter wire, (100 cm) ?. If Y = 0, then Equation (7) leads to X ? = (9) l 2 ? l1 Thus if Y is effectively a short circuit, then we can determine the resistance per unit length from knowledge of X and the measured values of l1 and l2. Learning Outcomes After studying the preparatory material, performing the experiments and working out the results, you should be able to 1.

Describe a Carey Foster bridge circuit, and explain how it can be used to measure an unknown resistance. 2. Explain some of the advantages and limitations of a Carey Foster bridge for measuring resistance. 3. Distinguish between a Carey Foster bridge and a meter bridge. 4. Use a Carey Foster bridge to determine the resistance per unit length of the bridge wire and to determine the value of an unknown resistance. 5. Explain the meaning of the terms in the glossary, and use them appropriately. Pre-lab Assessment Answer the following questions (1) (2) (3) (4) What is Wheatstone’s bridge?

When is the Wheatstone’s bridge most sensitive? Which other instruments based on the principle of Wheatstone’s bridge are used to determine resistances? Why is fractional resistance box used in this experiment? Procedure The experiment is performed in two parts. Part I Determination of resistance per unit length, ? , of the Carey Foster bridge wire 1. Make the circuit connections as shown in Figure 3. In this part of the experiment Y is a copper strip that has negligible resistance and X is a fractional resistance box.

You need to (a) ensure that the wires and copper strip are clean and the terminals are screwed down tightly, (b) remove any deposits from the battery terminals and (c) close tightly all of the plugs in the resistance box; these precautions will minimize any contact resistance between the terminals and the connecting wire. 2. Plug in the battery key so that a current flows through the bridge. Note that you should remove the battery plug when you are not taking measurements so that the battery does not become drained. 3.

Press down the jockey so that the knife edge makes contact with the wire, and observe the galvanometer deflection. Release the jockey. 4. Move the jockey to different positions along the wire and repeat step 3 at each place until you locate the position of the null point, where there is no deflection of the galvanometer. This point should be near the middle of the bridge wire. Take care that the jockey is pressed down gently to avoid damaging the wire and distorting its cross section, and do not move the jockey while it is in contact with the wire. 5.

Note the balancing length, l1, in your laboratory notebook, using a table with the layout shown in Table 1. 6. Reverse the connections to the terminals of the battery and record the balancing length for reverse current in the table in your notebook. By averaging readings with forward and reverse currents, you will be able to eliminate the effect of any thermo emfs. 7. Take out the plug from the fractional resistance box that inserts a resistance of 0. 1 ? , and repeat steps 3 – 5. 8. Increase resistance X in steps of 0. 1 ? and repeat steps 3 – 5 each time. 9.

Interchange the copper strip and fractional resistance box, and repeat steps 3 – 5 for the same set of resistances. The corresponding balancing lengths, measured from the same end of the bridge wire, should be recorded as l2 in your data table. Part II Determination of an unknown low resistance Y 1. Remove the copper strip and insert the unknown low resistance in one of the outer gaps of the bridge. 2. Repeat the entire sequences of steps as described in the procedure for the first part of the experiment. Record your measurements in your laboratory notebook.

A suggested format is shown in Table 2. Observations Table 1: Determination of ? for Carey Foster bridge wire S. No. X/ ? Position of balance point with copper strip in the right gap, l1 / cm left gap, l2 / cm direct reverse mean direct reverse mean current current current current l2 – l1 / cm ? = X / (l2 – l1) /? Table 2: Determination of an unknown low resistance using a Carey Foster bridge. S. No. X/ ? Position of balance point with unknown resistance in the right gap, l1 / cm left gap, l2 / cm direct reverse mean direct reverse mean current current current current l2 – l1 / cm

Y = X ? ? ( l2 – l1 ) /? Calculations 1. Determine an average value for (l2 – l1) for each value of X from each row of data in your version of Table 1. 2. Then calculate values of ? for the bridge wire from these values of (l2 – l1), using the formula ? = X / (l2 – l1). 3. Use these results to calculate a mean value of ? in SI units. 4. Use Equation (8) to calculate a value of the unknown resistance Y from each row of data in your version of Table 2. 5. Then use these results to calculate a mean value of Y. Results 1. The resistance per unit length of the bridge wire ? …… ? m-1. 2. The value of the unknown low resistance % error =………. Y = ……….. ? Actual value (if known) = ………. ? Possible sources of error • • • • The ends of connecting wires, thick copper strips and leads for the resistance box may not be clean, so there may be an additional contact resistance at the connections. The plugs of the fractional resistance box may be loose, again introducing undesirable contact resistance. The bridge wire may get heated up due to continuous passage of current for a long time. This will change its resistance.

If the jockey is not pressed gently or if it is kept pressed on to the wire while being shifted from one point to another, that may alter the cross sectional area of the wire and make it non uniform. Glossary Balance point (of a Carey Foster bridge): A point on the bridge wire that produces zero deflection in the galvanometer when the jockey knife edge is in contact with it. Also known as a null point. Carey Foster Bridge: a bridge based on the principle of Wheat stone’s bridge that is used to compare two nearly equal resistances and to determine values of low resistances and the specific resistance of a wire.

It differs from a meter bridge because additional resistances of similar magnitudes are included at either end of the meter wire. end correction (for a Carey Foster bridge): A small resistance that includes contributions from the finite resistance of the fixed copper strips within a Carey Foster bridge, the resistance at the junctions of the bridge wire with the copper strips and the effects of the non coincidence of the ends of the wire with the zero and one hundred division marks on the scale. Fractional resistance box: A box containing a number of fixed small resistance coils (0. -1. 0 ? or 0. 01-0. 1 ? ), so mounted that any number of these resistance coils can be connected in series. Galvanometer: An instrument used to detect current. In the Carey Foster bridge experiments, a very sensitive galvanometer is used, with zero current corresponding to the center of the scale. jockey: A metal knife edge mounted in plastic handle that can move along the bridge wire of a Carey Foster bridge and is used to locate the null point. Pressing on the jockey makes a point contact with the bridge wire. low resistance: A resistance in the range of 1-5 ohm. eter bridge: The most commonly used form of the Wheatstone’s bridge. It includes a uniform 1m long wire fixed on a wooden board, and it can be used for comparison of the values of two similar resistances. null point (of a Carey Foster bridge): A point on the bridge wire that produces zero deflection in the galvanometer when the jockey knife edge is in contact with it. Also known as a balance point. post office box: A compact form of Wheatstone’s bridge in which two of the arms contain resistances of 10, 100 or 1000 ?.

A third arm contains resistances from 1-5000 ? , and an unknown resistance can be connected in the fourth arm. Tapping keys are provided for connections to a galvanometer and battery. resistance: The opposition offered to the flow of current by an object. If a current I flows through an object when a potential difference V is connected across it, then the resistance R is given by R = V/I. The SI unit of resistance is the ohm, ?. specific resistance (of a wire): The resistance per unit length of the wire. In SI units, this is measured in ? m-1.

Wheatstone’s bridge: A bridge circuit (depicted in Figure 1) that comprises four resistances P, Q, R and S joined together to form a quadrilateral, with a battery connected across terminals at two opposite corners of the quadrilateral and a galvanometer between the other two corners. When the bridge is balanced (no current through the galvanometer), then P/Q = R/S. Post-lab Assessment Answer the following questions (1) (2) (3) (4) (5) (6) (7) What is the advantage of measuring resistance by null method? Why do you perform your experiment with direct as well as with reverse current? What is the end correction?

Have you included “The end correction” in your calculation? Can we measure very low resistance accurately by this method? Is this method suitable for the measurement of very high resistance? Can a copper wire be used as a bridge wire? Answers to Pre-lab Assessment 1. 2. 3. 4. Wheatstone’s bridge is an arrangement of four resistances P, Q, R and S connected in the form of a bridge such that the bridge is balanced when the product of the resistances in the opposite arms is same. The bridge is most sensitive when the resistances of the four arms are nearly equal and are comparable to the galvanometer resistance.

Two most common lab instruments based on the principle of Wheatstone’s bridge are Meter Bridge and post office box. When the resistances in the outer gaps are interchanged, the shifting of the null point should be on the bridge wire itself. The resistance introduced should be less than the resistance of the bridge wire which is very small. Therefore, in order to have a sufficient number of observations, a fractional resistance box is used. Answers to Post-lab Assessment 1. 2. 3. Null method means zero current through the galvanometer. So the calibration of the galvanometer does not come into play.

To eliminate the effect of current due to thermo e. m. f. This is due to the finite resistance of the copper strips fixed within the Carey Foster’s bridge, the resistance at the junctions of the wires with the copper strips and the non coincidence of the ends of the wire with the zero and hundred division marks on the scale. The error due to end correction do not appear in this method of measurement since the difference of the lengths between the null points is involved. No, because thermoelectric voltages developed at the junctions of dissimilar metals may cause problems when low resistances are measured.

The resistances of leads and contacts external to the bridge circuit may also affect measurements of very low resistances. No, since copper has a low specific resistance and a high temperature coefficient. Very high resistances cannot be measured very accurately with a standard Wheatstone bridge due to leakage of currents. That is current leakage in the electrical insulation may be comparable to the current in the branches of the bridge circuit when high resistances are measured. The sensitivity of the bridge to balance is also reduced for high resistances. 4. 5. 6. 7.