CAREY FOSTER
© Institute of Lifelong Learning, University of Delhi
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CAREY FOSTER
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PHYSICS (LAB MANUAL)
© Institute of Lifelong Learning, University of Delhi
PHYSICS (LAB MANUAL)
CAREY FOSTER
Introduction
The Carey Foster’s 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.
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PHYSICS (LAB MANUAL)
CAREY FOSTER
Apparatus
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Carey Foster’s 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
Jockey
fractional
resistance box
lead accumulator
standard
resistances
bridge wire
galvanometer
Figure 2:
Experimental setup for the Carey Foster’s bridge.
Theory
The aim of the experiment is to determine the resistance per unit length, ρ of the
Carey Foster’s 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.
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PHYSICS (LAB MANUAL)
CAREY FOSTER
Figure 3: Circuit diagram for the Carey Foster’s 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 comparable 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
 
Q S Y    100  l1  
(2)
where α and β 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
 
Q S X    100  l 2  
(3)
Combining Equations 2 and 3, we obtain
 X    l1    Y    l 2  
Y    100  l1  X    100  l 2  
(4)
Adding 1 on both sides and simplifying,
 X    Y    100  Y    X    100 

Y    100  l1    X    100  l2  
(5)
Since the numerators are equal, we can write
Y    100  l1   X    100  l 2  ,
X  Y  l 2  l1  ,
Y  X  l 2  l1 
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(6)
(7)
(8)
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PHYSICS (LAB MANUAL)
CAREY FOSTER
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, ρ and 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
l 2  l1
(9)
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’s 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’s bridge for
measuring resistance.
3. Distinguish between a Carey Foster’s bridge and a meter bridge.
4. Use a Carey Foster’s 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
Now to know whether you are ready to carry out the experiment in the
lab, answer the following questions. If you score at least 80%, you are
ready, otherwise read the preceding text again. (Answers are given at
the end of this experiment.)
(1) What is Wheatstone’s bridge?
(2) When is the Wheatstone’s bridge most sensitive?
(3) Which other instruments based on the principle of Wheatstone’s bridge are
used to determine resistances?
(4) 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, ρ, of the Carey
Foster’s 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
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PHYSICS (LAB MANUAL)
CAREY FOSTER
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 Ω, and repeat steps 3 – 5.
8. Increase resistance X in steps of 0.1 Ω 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 sequence 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’s bridge wire
S. No.
X/
Position of balance point
right gap, l1 / cm
direct
reverse
mean
current
current
with copper strip in the
left gap, l2 / cm
direct
reverse
mean
current
current
l2 – l1
/ cm
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 = X / (l2 – l1)
Ω/cm
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PHYSICS (LAB MANUAL)
CAREY FOSTER
Table 2: Determination of an unknown low resistance using a Carey
Foster’s bridge.
Position of balance point with unknown resistance in the
S. No.
X/
right gap, l1 / cm
direct
reverse
mean
current
current
left gap, l2 / cm
direct
reverse
current
current
mean
l2 – l1
/ cm
Y = X (l2 – l1)
/Ω
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 ρ 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
 = …… Ω m-1.
2. The value of the unknown low resistance
Y = ……….. Ω
Actual value (if known) = ………. Ω
% error =……….
Possible sources of error
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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’s 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.
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PHYSICS (LAB MANUAL)
CAREY FOSTER
Carey Foster’s 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’s bridge): A small resistance that includes
contributions from the finite resistance of the fixed copper strips within a Carey
Foster’s 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 (0.1-1.0 Ω or 0.01-0.1 Ω), 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’s
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’s 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.
meter 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’s 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 Ω. A third arm contains resistances
from 1-5000 Ω, 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) What is the advantage of measuring resistance by null method?
(2) Why do you perform your experiment with direct as well as with
reverse current?
(3) What is the end correction?
(4) Have you included “The end correction” in your calculation?
(5) Can we measure very low resistance accurately by this method?
(6) Is this method suitable for the measurement of very high
resistance?
(7) Can a copper wire be used as a bridge wire?
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CAREY FOSTER
PHYSICS (LAB MANUAL)
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.
4.
5.
6.
7.
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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.
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.
No, since copper has a low specific resistance and a high temperature
coefficient.
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