1 Bridges-Part-I

Vinay Gupta

epgp books

 

    Learning Objectives

In this module we will study about various kinds bridge circuits.

  1. First we will study about Bridge Control Circuits and various types bridges that are used for measuring unknown resistance.
  2. Under DC Bridges will study about Wheatstone bridge, its circuit design and its sensitivity
  3. Then we will study about Kelvin double bridge and how it is used for measuring resistances less than 1 ohm.

   Introduction

 

This module is aimed to study various methods involved in measurement of unknown resistance. The choice of suitable method for measurement of resistance depends on number of factors. First would range of resistance to be measurement, i.e. low, medium and high. Other factor may be required for accuracy of measurement, working conditions, etc. Another important factor to be considered is the resistance of the conducting material with rise in temperature as well as absorption of moisture, where material is hygroscopic. From the point of view of measurements, resistances can be classified as –

 

 (i) Low Resistances. Resistance of 1 ohm and under are included in this category. Measurement of low resistances is required for determination of resistance of armatures, and series field windings of large machines, ammeter shunts, cable lengths, contacts, etc.

 (ii) Medium Resistances. Resistances ranging from 1 to 100 k fall into this category. 

(iii) High Resistances. Resistances above 100 k are included in this class. The measurement of high resistances is required for determination of (a) Resistance of high resistance circuit elements; (b) Insulation resistance of components and built-up electrical equipment of all types;(c) Volume resistivity of the material and (d) Surface resistivity.

For measurement of resistances belonging to the above-discussed categories various bridge-controlled circuits are used.

 

Bridges Controlled Circuit

 

A Bridge controlled circuit is an electrical circuit where two parallel branches are interlinked via by a third branch at an intermediate point between the parallel branches. Initially bridge circuits were designed for laboratory purposes but now similar circuits are used for linear & non-linear measurements, power conversion, instrumentation and filtering. In simpler terms, besides measuring impedances, bridge circuits are also used for altering signals from transducers with associated current and voltage signals

 

There 2 types of bridge circuits –

 

(1)  D.C. Bridges – They use D.C voltage and are used for measuring resistances whereas

 

(2) A.C Bridges are used over alternating voltage (A.C. circuits) and measure impedances consisting capacitances and inductances.

 

There are 2 types of D.C. bridge-

 

1.  Wheatstone Bridge 2. Kelvin Bridge

 

And

 

The various types of A.C. bridges are –

1. Capacitance comparison bridge      2. Wein Bridge

3. Inductance Comparison Bridge      4. Resonance Bridge

 

D.C. Bridges

 

Wheatstone Bridge

 

The earliest example of bridge circuit is Wheatstone Bridge. In 1833, it was Samuel Hunter Christie who came up with the concept of bridge circuit which was known as Diamond method due diamond like shape of the electrical circuit. It was 10 years later in 1843 Charles Wheatstone introduced few modifications and promoted it as a better method to measure resistance of an unknown resistor. Besides digital multimeters, a Wheatstone bridge can be used for measuring resistances down to milli-ohms range. Circuit diagram for the Wheatstone bridge can be seen in figure 1.

Figure. 1 – A typical Wheatstone bridge cicuit

 

A Wheatstone bridge consists of four resistors, where R1 and R3 are of know values, R2 is variable resistor and Rx is the resistor whose resistance is to be determined. The branch that interlinks the two branches has Galvanometer Vg to measure current flow between the two branches. If the current between the two branches is not zero, variable resistor is adjusted to bring the current flow to zero between point D & B. Now, according to Kirchhoff’s second law the net voltage in the loops ABDA and

 

BCDB should be equal to zero. The equation for both loops can be written as For loop ABDA

 

(I3.R3) – (Ig.Rg) – (I1.R1) = 0 —-(1)

 

For loop BCDB

 

(IX.RX) – (I2.R2) + (Ig. Rg) = 0   ——(2)

 

when net flow between point D & B is zero, i.e. when bridge is balanced, Ig=0, then

 

I3.R3 = I1.R1 —-(3)

 

and

 

IX.RX = I2.R2  ——(4)

 

Now according to Kirchhoff’s first law the net current at point B is given by

 

I3 – IX + Ig = 0 —–(5)

 

and at point D is given by

 

I1 – I2 – Ig = 0   ——(6)

 

Therefore when bridge is balanced and equation 3 & 4 are divided and as we rearranged them, we get –

 

Briefly, the values of unknown resistor Rx can be determined when values of other three resistors R1,R2, R3 are know to us. It should be noted that the relationship between the resistances will still hold true even if battery and galvanometer are interchanged.

 

Now we look into the advantages of the Wheatstone bridge.

 

Advantages

 

Since the net current across point B &D is null (zero), this type of DC bridge is also known as null type DC bridge. Here inaccuracies that may arise due instrument calibration can be easily avoided as galvanometer is simply used for measuring zero current. Another advantage of this method is that any errors due to fluctuations in emf source can be avoided, as the balance of current is quite independent of the emf source. At reduced sensitivity, this system has range of resistance from 1 to 10,000 ohms and can be further extended.

 

Precautions– that should be taken when working with a wheatstone bridge While measuring an unknown resistor one should take the following precautions

  1. Galvanometer should be well shunted, in order to avoid violent deflection during early stages of balancing operation and one should reduce the shunt resistance as bridge approaches the balancing position. This also increases sensitivity of galvanometer.
  2. One should always switch off battery before the galvanometer key and open after it; this will reduce any induced emfs due to rapidly changing current in case resistor under test is inductive. This too will prevent any violent deflections in galvanometer
  3. Measurements should also be conducted by reversing the battery and mean of two should be taken as correct value. This will avoid any errors due to thermoelectric emfs.

Now we look into the Sensitivity of the system

 

Sensitivity of Wheatstone Bridge 

 

In a slightly unbalanced bridge, sometimes it is desirable to know galvanometer response. This helps in selecting a galvanometer sensitive to unbalance in a specific bridge arrangement. It is used to determine minimum unbalance that can be observed with a given galvanometer for a specified bridge plus it helps in determining minimum deflection to be expected for a given unbalance.

 

Figure. 2 – A Wheatstone Bridge

 

By solving bridge circuit for the small unbalance one can calculate Bridge sensitivity, SB. Let us assume bridge in figure 2 is perfectly balanced such that

 

and to create small unbalance, the resistance of R is changed to R + R. Then open circuit voltage (e) for the given bridge can be written as

 

For a balanced bridge, while solving for the above equation, the second and higher order terms in power expansion may be neglected.

 

Now the Voltage Sensitivity Sv of a galvanometer is defined as the change in scale units per unit change in voltage in the galvanometer circuit when the total resistance, seen from the galvanometer circuit, is that required for the specified damping,

 

Therefore, the bridge Sensitivity SB can be defined as the deflection of the galvanometer per unit fractional change in the unknown resistance, which can be written as

 

   Now we look into a variant of wheatstone bridge- that is kelvin bridge

 

Kelvin Bridge

 

Minimum resistance that can be measure accurately with Wheatstone bridge is 1 ohm. To measure a resistor having value below 1 ohm a Kelvin Bridge is used. A Kelvin bridge is also know as Kelvin double bridge and Thomson bridge is some countries. A Kelvin bridge has two extra resistors that form a second set of ratio arms, hence named double bridge. This modification eliminates the effect of contact and lead resistance while measuring a low resistance. Here resistors within the range of 1 ohm to approximately 1 micro-ohm can be measured with high accuracy. This modified form of Wheatstone bridge is shown in the following figure 3.

Figure 3. Circuit Diagram for Kelvin Bridge

 

Here X is the resistor of unknown resistance and Resistor S is a standard resistor of same order of resistance and the same or the higher current rating as compared to resistor under test. P, Q and small p,q are non-inductive resistors with two ratio arms similar to Wheatstone bridge interlinked via galvanometer G between points F & K. A Rheostat along with an Ammeter is there for convenience only.

 

During the measurement ratios P/Q and small p/q are varied until galvanometer reads zero. When both the ratio arms are balanced we get the following equations according to the Kirchhoff’s second law for the two meshes AHFKBA and FEDCKF –

 

I1.P – I2.p – I.X = 0 ——-(12)

This can be written as

Or I.X = I1.P – I2.p ——-(13)

 

And I1.Q –I2.q –I.S =0 ——– (14)

This can be written as

Or I.S = I1.Q – I2.q ——–(15)

 

By dividing equation 13 & 15 we get –

    Hence the value of unknown resistance X = S. (P/Q) ———– (16)    Operation of Kelvin Double Bridge

 

The method of operation of the kelvin bridge is slightly different from what is described earlier for wheatstone bridge. During the measurements, P,Q, small p & q are know and fixed standard resistances and their temperature coefficients are also know. The resistance are of such values that P/Q=small p/q. Here, P is taken equal to small p and Q is taken equal to small q and the ratio P/Q= small p/q is made approximately equal to X/S.

 

In case approximate value of X is unknown, then it can be either determined with voltmeter –ammeter method or by potentiometer method. Thereafter, the unknown resistance X is shunted by a variable resistance (whose value is known) and to obtain the balance, the value of the shunting resistance is adjusted.

 

With shunting of unknown resistance X by a variable resistance of value r, a balance is obtained and the equation 16 can be written as-X prime

  In this equation the values of P,Q,R,S and r are known, therefore value of unknown resistance can be determined by substituting these values.

 

Here again the supply current is reversed and the average value from the two observations may be taken as correct value. This helps in eliminating any errors due to thermo-electric emfs.

 

The bridge’s sensitivity is determined by noting the smallest variation in the shunting resistance r that can cause an observable deflection in the galvanometer. The ratios P/Q & small p/q are made exactly equal by adjusting the lead resistances, which are used for the connections.

 

Summary

 

In this module we studied about various kinds bridge circuits.

  1. First we looked into Bridge Control Circuits and various types bridges that are used for measuring unknown resistance.
  2. Under DC Bridges will studied about Wheatstone bridge, its circuit design and its sensitivity
  3. And in the end we studied about Kelvin double bridge and how it is used for measuring resistances less than 1 ohm.
you can view video on Bridges-Part-I

    References :-

  1. Electrical and Electronic Measurements and Instrumentation, Sawhney A. K., Dhanpat Rai & Sons, Reprint 1985
  2. Measurements and Instrumentation, Bakshi U.A., Bakshi A.V., Technical Publications, 2009
  3. Principles of instrumental analysis, Skoog, Douglas A., F. James Holler, and Stanley R. Crouc,. Cengage learning, Edition 2017
  4. Instrumentation, measurement and analysis. Nakra, B.C. and Chaudhry, K.K., Tata McGraw-Hill Education, 2003.
  5. Measurement and instrumentation: theory and application, Morris, A. S., & Langari, R. , Academic Press, 2012.