Carey Foster Bridge Construction & Working Principle

Hi friends, this post provides an information about Carey Foster bridge. We will also learn how this bridge can be used to determine the resistance in detail with deriving an expression for determining resistance.

Carey-Foster bridge Experiment

We have already seen some basic methods for measuring medium resistances. Carey foster bridge is the method used for measurement of medium resistances. Carey foster bridge is specially used for the comparison of two equal resistances. The circuit for Carey-Foster Bridge is shown in figure below. A slide wire having length L is included between R and S. resistance P and Q are adjusted so that the ratio P/Q is approximately equal to R/S. this can be achieved by sliding contact on slide wire.

Carey foster bridge method
Carey foster bridge circuit

Carey Foster Bridge: Working Principle

The working principle of Carey Foster bridge is similar to the Wheatstone bridge. The potential fall is directly proportional to the length of wire.This potential fall is nearly equal to the potential fall across the resistance connected in parallel to the battery.

Description:

Let l1 be the distance of the sliding contact from the left hand end of the slide-wire of Carey foster bridge. The resistance R and S are interchanged and balance is again obtained. Let the distance is now l2.

Let r= resistance/unit length of slide wire

For first balance,

Carey foster bridge method 1

For second balance,

Carey foster bridge method 2

Comparing,

Carey foster bridge method 3

Where l1 and l2 are balanced points when slide wire is calibrated by shunting S with a known resistance and S’ is value of S when it is shunted by a known resistance. Thus Carey foster bridge can be used to measure the medium resistance.

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Maxwell’s inductance capacitance bridge

Maxwell’s inductance capacitance bridge:

In Maxwell’s inductance capacitance bridge the value of inductance is measured by the comparison with standard variable capacitance. The connection for Maxwell’s inductance capacitance bridge is shown in figure below.

maxwell's inductance capacitance bridge for measurement of inductance
maxwell’s inductance capacitance bridge for measurement of inductance

Let

L1=unknown inductance,

R1=effective resistance of inductor L1,

R2, R3, R4=known noninductive resistances,

C4=variable standard capacitor.

And writing the equation for balance

1

Separating the real and imaginary terms, we have

2

Thus we have two variables R4 and C4 which appear in one of the two balance equations and hence the two equations are independent.

The expression for Q factor

3

Advantages of Maxwell’s inductance capacitance bridge:

1)      The two balance equations are independent if we choose R4 and C4 as variable elements.

2)      The frequency does not appear in any of the two equations.

3)      This bridge yields simple expressions for L1 and R1 in terms of known bridge elements.

Disadvantages of Maxwell’s inductance capacitance bridge:

  • This bridge requires a variable standard capacitor which may be very expensive if calibrated to the high degree of accuracy. Therefore sometimes a fixed standard capacitor is used, either because a variable capacitor is not available or because fixed capacitors have a higher degree of accuracy and are less expensive than the various ones. The balance adjustments are then done by:

a)      Either varying R2 and R4 and since R2 appears in both the balance equations, the balance adjustments become difficult; or

b)      Putting an additional resistance in series with the inductance under measurement and then varying this resistance and R4.

  • The bridge is limited to the measurement of low Q coils (1<Q<10). it is clear from the Q factor equation that the measurement of high Q coils demands a large value of resistance R4, perhaps 10^5 or 10^6 O. The resistance boxes of such high values are very expensive. thus for values of  Q>10, the Maxwell’s bridge is unsuitable.

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Maxwell’s inductance bridge

Maxwell’s inductance bridge:

Maxwell’s inductance bridge measures the value of given inductance by comparison with a variable standard self inductance. The circuit diagram of Maxwell’s inductance bridge is shown in figure below.

Maxwells inductance bridge for measurement of inductance
Maxwells inductance bridge for measurement of inductance

Let

L1 = unknown inductance of resistance R1,

L2 = variable inductance of fixed resistance r2,

R2 = variable resistance connected in series with inductor L2,

R3, R4 = known non-inductive resistances.

At balance,

1

Resistance R3 and R4 are normally a selection of values from 10, 100, 1000 and 10,000O. r2 is decade resistance box. In some cases, an additional known resistance may have to be inserted in series with unknown coil in order to obtain balance.

Let us solve one simple problem for clear understanding of Maxwell’s inductance bridge.

Problem:

A Maxwell’s inductance comparison bridge is shown in the figure above. Arm ab consists of a coil with inductance L1 and resistance r1 in series with a non-inductive resistance R. arm bc and ad are each a non-inductive resistance of 100O. Arm ad consists of standard variable inductor L of resistance 32.7O. Balance is obtained when L2 = 47.8mH and R = 1.36O. Find the resistance and inductance of the coil in arm ab.

Solution:

At balance [(R1+r1)+jwL1]*100 = (r2+jwL2)*100

Equating the real and imaginary terms

R1+r1 = r2 and L2=L1

Therefore, resistance of coil:

r1 = r2 – R1 = 32.7 – 1.36 = 31.34O.

Inductance of coil:

L1 = L2 = 47.8mH.

tags: maxwell’s inductance bridge ppt pdf maxwell’s bridge theory anderson bridge for the measurement of inductance. maxwell bridge experiment applications uses and disadvantages and advantages of maxwell inductance bridge.

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Kelvin double bridge circuit for measurement of low resistance

In this post we will see the Kelvin double bridge. It is used for the measurement of low resistances. The Kelvin double bridge is the modification of the Wheatstone bridge and provides greatly increased accuracy in measurement of low value resistance.

An understanding of the Kelvin bridge arrangement may be obtained by the study of the difficulties that arise in a Wheatstone bridge on account of the resistance of the leads and the contact resistances while measuring low valued resistance.

The Kelvin double bridge incorporates the idea of a second set of ratio arms-hence the name double bridge-and the use of four terminal resistors for the low resistance arms.

Figure shows the schematic diagram of the Kelvin bridge. The first of ratio arms is P and Q. the second set of ratio arms, p and q is used to connect the galvanometer to a point d at the appropriate potential between points m and n to eliminate effect of connecting lead of resistance r between the unknown resistance, R, and the standard resistance, S.

The ratio p/q is made equal to P/Q. under balance conditions there is no current through the galvanometer, which means that the voltage drop between a and b, Eab is equal to the voltage drop Eamd.

kelvin double bridge
kelvin double bridge

Now the voltage drop between a and b is given by,

1 2

for bridge to be balance3

Above equation is the usual working equation for the Kelvin Double Bridge. It indicates that the resistance of connecting lead, r, has no effect on the measurement, provided that the two sets of ratio arms have equal ratio. The former equation is useful, however, as it shows the error that is introduced in case the ratios are not exactly equal. It indicates that it is desirable to keep r as small as possible in order to minimize the errors in case there is a difference between ratios P/Q and p/q.

solution:

 

Photo0103

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Wheatstone Bridge Method for Measurement of Resistance

Another method of measuring the value of a resistor is the Wheatstone bridge. This device sets up a parallel resistor system that measures the differences in voltage between two legs of a circuit. If there is a difference of voltage between the branches it will be detected by the galvanometer. A special type of Wheatstone bridge is a slide wire bridge. The setup for a slide wire bridge is shown in Figure 1. In this case, there is a wire of constant resistivity with a contact that can move over the entire length.

Wheatstone bridge method for measurement of resistance
Wheatstone bridge method for measurement of resistance

The resistance of the lengths of wire created by moving the contact is proportional to the length of the wire. So, expressing the resistance in terms of the wire length we have,
R2/R1 = L2/L1
If you are trying to determine the resistance of an unknown resistor and you have a known resistance available, the value of the unknown resistor is,
R2 = (L2/L1) R1
Where R1 is a specified resistance.

Procedure

Ammeter – Voltmeter Method

  1. Measure the resistance of an unknown resistor using an ohmmeter.
  2. With the help of your instructor set up a circuit using the unknown resistor as
    shown in Figure 1. Turn on the power.
  3. Measure the current flowing through the resistor.
  4. Measure the voltage across the resistor
  5. Calculate the value of the unknown resistor using Ohm’s Law.
  6. Find the % difference between your two values.

Wheatstone Bridge Method

  1. Set up a slidewire bridge circuit as shown in Figure.
  2. The wires connecting the resistances and the bridge should be as short as practically possible. Use a decade box with a known resistance as R1. This should be set to a value about equal to R2 (as measured by an ohmmeter). You can test this value by changing the decade box resistance and testing the bridge balance point until it is near the center of the bridge. Contact is made to the wire by sliding contact key C. Do not slide the key along with the wire while it is pressed down. This will scrape the wire causing it to be nonuniform. Have the instructor check your wiring before activating the circuit.
  3. Activate the circuit by closing the switch S, and balance the bridge by moving the slide wire contact. Open the switch and record R1, L1, and L2. Leave the switch open unless actually making measurements.
  4. Repeat procedure 1 for R1 settings of (a) R1 ??3 R2 and (b) R1 ??0.3 R2 .
  5. Compute the value of R2 for each case and find the average value. Compare this value to the directly measured value of R2 by finding the percent difference.
  6. Repeat the previous procedures with a large known resistance R1 and record your findings.

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Megohm Bridge Method for Measurement of Resistances

Megohm bridge is another important method for measurement of high resistances. It has one three terminal high resistance located in one arm of the bridge.

Fig a) shows the very high resistance with terminals A and B, and a guard terminal, which is put on the insulation. So it forms a three terminal resistance.

Megohm bridge three terminal resistance
Megohm bridge three terminal resistance

Let us consider take the hypothetical case of a 100 Mohm resistance .let we assume that this resistance is measured by an ordinary Wheatstone bridge. It is clear that Wheatstone will measure a resistance of 100*200/(100+200)=67Mohm instead of 100Mohm thus the error is 33 percent.

Megohm Bridge method for measurement of resistances
Megohm Bridge method for measurement of resistances

However, if the same resistance is measured by a modified Wheatstone bridge as shown in fig b)with the guard connection G connected as indicated, the error in measurement will be reduced and this modified Wheatstone bridge is called megohm bridge.

The arrangement of above figure illustrated the operation of Megohm Bridge.

The figure shows the circuit of the completely self-contained Megohm Bridge which includes power supplies, bridge members, amplifiers, and indicating instrument. It has ranged from 0.1MO to 10^6MO. The accuracy is within 3% for the lower part of the range to possible 10% above 10000MO.

The sensitivity of balancing against high resistance is obtained by use of adjustable high voltage supplies of 500V or 1000V and the use of a sensitive null indicating arrangements such as a high gain amplifier with an electronic voltmeter or a C.R.O. The dial on Q is calibrated 1-10-100-1000 MO, with main decade 1-10 occupying greater part of the dial space. Since unknown resistance R=PS/Q, the arm Q is made, tapered, so that the dial calibration is approximately logarithmic in the main decade, 1-10. Arm S give five multipliers, 0.1,1,10,100 and 1000.

The junction of ratio arms P and Q is brought on the main panel and is designated as ‘Guard’ terminal.

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Loss of Charge Method for Measurement of Resistances

loss of charge method
Loss of charge method for measurement of resistances

In the loss of charge method unknown resistance is connected in parallel with the capacitor and electrostatic voltmeter. The capacitor is initially charged to some suitable voltage by means of a battery of voltage V and then allowed to discharge through the resistance. The terminal voltage is observed during discharge and it is given by,

V=v exp (-t/CR)

OR

V/v = exp (-t/CR)

Or insulation resistance is given by,

R= t/(C ln V/v)

= 0.4343 t / (C log V/v)

The variation of voltage v with time is shown in figure,

Loss of Charge Method Plot
Loss of Charge Method Plot

From above equation, it follows that if V, v, C, and t are known the value of R can be computed.

If the resistance R is very large the time for an appreciable fall in voltage is very large and thus this process may become time-consuming. Also the voltage-time curve will thus be very flat and unless great care is taken in measuring voltages at the beginning and at the end of time t, a serious error may be made in the ratio V/v causing the considerable corresponding error in the measured value of R. more accurate results may be obtained by change in the voltage V-v directly and calling this change as e, the expression for R becomes:

123

This change in voltage may be measured by a galvanometer.

However, from the experimental point of view, it may be advisable to determine the time t from the discharge curve of the capacitor by plotting the curve of log v against time t. this curve is linear as shown in the second figure and thus the determination of time t from this curve for the voltage to fall from V to v yields more accurate results.

Loss of charge method is applicable to some high resistances, but it requires a capacitor of very high leakage resistance as high as resistance being measured. The method is very attractive if the resistance being measured is the leakage resistance of a capacitor as in this case auxiliary R and C units are not required.

Actually, in this method, we do not measure the true value of resistance since we assume here that the value of resistance of electrostatic voltmeter and the leakage resistance of the capacitor have infinite value. But in practice corrections must be applied to take into consideration the above two resistances. Let R1 be the leakage resistance of the capacitor. Also R’ be the equivalent resistance of the parallel resistances R and R1.

loss of charge method with leakage resistance of capacitor
loss of charge method with leakage resistance of the capacitor

Then discharge equation of capacitor gives,

R’=0.4343 t / (C log V/v)

The test is then repeated with the unknown resistance R disconnected and the capacitor discharging through R1. The value of R1 obtained from this second test and substituted into the expression,

R’=(R R1) / (R+R1)

In order to get the value of R.

The leakage resistance of the voltmeter, unless very high should also be taken into consideration.

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Substitution Method For Measurement Of Medium Resistance

The connection diagram for substitution method is shown in fig. below. R is the unknown resistance to be measured, S is the standard variable resistance, ‘r’ is the regulating resistance and ‘A’ is an ammeter. There is a switch for putting S and R in a circuit.

Substitution Method For Measurement Of Medium Resistance
Substitution Method For Measurement Of Medium Resistance

Firstly switch is at position 1 and R is connected in a circuit. The regulating resistance ‘r’ is adjusted till ammeter pointer is at chosen scale. Now switch is thrown to position ‘2’ and now ‘S’ is in a circuit. The value of standard variable resistance ‘S’ is varied till the same deflection as was obtained with R in the circuit is obtained. When the same deflection obtained it means same current flow for both the resistances. It means resistances must be equal. Thus we can measure the value of unknown resistance ‘R’ by substituting another standard variable resistance ‘S’. Therefore this method is called Substitution method.

This is more accurate method than ammeter-voltmeter method. The accuracy of this method is greatly affected if the emf of the battery changes during the time of readings. Thus in order to avoid errors on this account, a battery of ample capacity should be used so that the emf remains constant.

See also: Ammeter voltmeter method.

The accuracy of the measurement naturally depends upon the constancy of the battery emf and of the resistance of the circuit excluding R and S, upon the sensitivity of the instrument, and upon the accuracy with which standard resistance S is known.

This method is not widely used for simple resistance measurements and is used in a modified form for the measurement of high resistances. The substitution principle, however, is very important and finds many applications in bridge methods and in high-frequency a.c. measurements.

Example

In a measurement of resistance by substitution method, a standard 0.5MO resistor is used. The galvanometer has a resistance of 10KO and gives deflections as follows:

1) With standard resistor, 41 divisions,

2) with unknown resistance, 51 divisions.

Find the unknown resistance.

Solution

The deflection of the galvanometer is directly proportional to the current passing through the circuit and hence is inversely proportional to the total resistance of the circuit. Let S, R, and G be respectively the resistances of the standard resistor, unknown resistor and galvanometer. Also, let ?1 be the deflection with a standard resistor in the circuit and ?2 with an unknown resistor in the circuit.

Hence unknown resistance R=(S+G)*?1/?2-G

= (0.5*10^6+10*1000)*(41/51)-10*1000

=0.4*10^6O

=0.4 MO.

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