Measurement of resistance

Hello friends, in this blog article we will learn different methods for the measurement of resistance. We will first see, what are the different types of methods in short and will explain the same in details in separate blog articles.

Measurement of Resistance

Before learning different types of methods for measurement of resistance, we will first see the classification of resistance. From the point of view of measurement, we have three types of resistances as follows:

  1. Low resistances: < 1Ω
  2. Medium resistances: 1Ω to 100,000Ω
  3. High resistances: >100,000Ω

A. Measurement of Low resistance

  1. Ammeter-Voltmeter method
  2. Kelvin’s double bridge method
  3. Potentiometer method
  4. Ducter

B. Measurement of Medium resistance

  1. Ammeter-Voltmeter method
  2. Substitution method
  3. Wheatstone bridge method
  4. Ohmmeter method

C. Measurement of High resistance

  1. Direct deflection method
  2. Loss of Charge method
  3. Megohm bridge
  4. Megger

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.

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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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Direct deflection method for high resistance

Direct deflection method:

Direct deflection method for measurement of high resistance
Direct deflection method for measurement of high resistance

The figure shows the measurement of high resistance using direct deflection method. For measurement of high resistance such as insulation resistance of cables, a sensitive galvanometer of d’Arsonval type is used in place of the microammeter. In fact many sensitive type of galvanometers can detect currents from 0.1-1nA.therefore, with an applied voltage of 1kV, resistance as high as 10^12 to 10*10^12O can be measured.

The first figure shows the direct deflection method for measurement of high resistance having metallic sheath. The galvanometer G shows the current between the conductor and the metallic sheath. The leakage current  is carried by the guard wire wound on the insulation and therefore does not flow through the galvanometer as shown in figure.

Cables without metal sheaths can be tested in a similar way if the cable, except the ends or ends on which connections are made, is immersed in water in a tank. the water and a tank then forms the return path for the current .the cable is immersed in slightly saline water for about 24 hours and the temperature is kept constant at about 20 degree Celsius and then the measurement is taken as shown in second figure

The insulation resistance of the cable is given by,

 1

In some cases, the deflection of the galvanometer is observed and its scale is afterwards calibrated by replacing the insulation by a standard high resistance (usually 1MO), the galvanometer shunt being varied, as required to give a deflection on the same order as before.

In tests on cable the galvanometer should be short-circuited before applying the voltage. The short-circuiting connection is removed only after sufficient time is elapsed so that charging and absorption currents cases to flow. The galvanometer should be well shunted during the early stages of measurement, and it is normally desirable to influence a protective series resistance (of several megaohm) in the galvanometer circuit. The value of this resistance should be subtracted from the observed resistance value in order to determine the true resistance. A high voltage battery of 500V emf is required and its emf should remain constant throughout the test.

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