CHAPTER 4 Bridge Measurement 1 Bridge InstrumentsCircuits A

CHAPTER 4 Bridge Measurement 1

Bridge Instruments/Circuits A circuit consists of a network of a four resistance arms forming a closed circuit with a DC source of current applied to two opposite junctions and a current detector connected to the other two junctions. 2

3

Measurement of Resistance ( ) DC Bridge ◦ Wheatstone Bridge ◦ Kelvin’s Bridge ◦ Mega-ohm Bridge 4

Wheatstone bridge A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer. It was invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. The Wheatstone bridge circuit is the most accurate method of measuring resistance and is used very widely wherever an accurate measurement is required. 5

Cont’… Consist of two parallel resistance branches with each branch containing two series resistors. A DC voltage source is connected across network to provide a source of current through resistance. A galvanometer (null detector is connected between parallel branches to detect a condition of balance. Suitable for resistance value 1 to 10 M 6

Cont’… At balance condition, no current flows through galvanometer Therefore, Voltage drop, 7

Example 1 Determine the value of unknown resistance, R 4 in a Wheatstone bridge if R 1 = 12 k , R 2 = 15 k and R 3 = 32 k. 8

Sensitivity of a Wheatstone Bridge When the bridge is in an unbalanced condition, current flows through the galvanometer causing the deflection of pointer. The amount of deflection is a function of sensitivity of the galvanometer. Sensitivity is deflection per unit current Can be expressed in linear or angular unit of measure. Sensitivity, S= mm/ A=degree/ A=radians/ A Total deflection, D = S x I ( A) 9

Thévenin's Theorem Thévenin's theorem for linear electrical networks states that any combination of voltage sources, current sources, and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems theorem can also be applied to general impedances, not just resistors. The theorem was first discovered by German scientist Hermann von Helmholtz in 1853, but was then rediscovered in 1883 by French telegraph engineer Léon Charles Thévenin (1857– 1926 10

Unbalanced Wheatstone Bridge Use the Thevenin’s Theorem 11

Cont’… Thevenin’s equivalent voltage, Vth 12

Cont’… Thevenin’s equivalent resistance, Rth R 1//R 3 & R 2//R 4 13

Cont’… If a galvanometer is connected to terminal a and b, the deflection current is the current through the galvanometer. Current through the galvanometer Rg is the internal resistance in the galvanometer. 14

Example 2 Calculate the current through the galvanometer in an unbalanced Wheatstone bridge. Given supply voltage is 6 V, R 1 = 1 k , R 2 = 1. 6 k , R 3 = 3. 5 k , R 4 = 7. 5 k and Rg = 200 , 15

Measurement Errors Limiting error of the known resistors Insufficient sensitivity of detector Changes in resistance of the bridge arms due to the heating effect (I²R) or temperatures Thermal emf or contact potential in the bridge circuit Error due to the lead connection 16

Slightly Unbalanced Wheatstone Bridge If three of the four resistors in a bridge are equal to R and the fourth differs by 5% or less, we can developed an approximate but accurate expression for Thevenin’s equivalent voltage and resistance. 17

Cont’… To find Rth An approximate Thevenin’s equivalent circuit 18

Example 3 a Use the approximation equation to calculate the current through the galvanometer in Figure below. The galvanometer resistance, Rg is 125 Ω and is a center zero 200 -0 -200μA movement. 19

Example 3 b In the Wheatstone bridge circuit, R 3 is a decade resistance with a specified inaccuracy ± 0. 2% and R 1 and R 2 = 500 Ω ± 0. 1%. If the value of R 3 at the null position is 520. 4Ω, determine the possible minimum and maximum value of Rx. 20

Kelvin’s Bridge A modified version of the Wheatstone bridge To eliminate the effects of contact and lead resistance when measuring unknown low resistances (<1 ) 21

Cont’… At point n: Ry is added to the unknown Rx, resulting in too high and indication of Rx, At point m: Ry is added to R 3, therefore the measurement of Rx will be lower than it should be. 22

Example 4 R 1 is 5Ω and R 1 = 0. 5 R 2. If the ratio of Ra to Rb is 1000. What is the value of Rx ? 23

Mega-ohm Bridge High resistance measurements are affected by shunt-leakage resistance. The guard terminal is connect to a bridge corner such that the leakage resistances are placed across bridge arm with low resistances Unknown resistor, 24

AC Bridge Capacitance Measurement All four arms are considered as impedance (Z) Source is an ac voltage at desired frequency At balance condition, Complex form Polar form 25

AC Bridge for Capacitance Measurement 26

Capacitance Measurement ◦ Capacitance Comparison Bridge ◦ Schering Bridge 27

Capacitance Comparison Bridge The condition for balance of the bridge 28

Cont’… 29

Example 5 A capacitance comparison bridge is used to measure a capacitive impedance at a frequency of 2 k. Hz. The bridge constants at balance are C 3 = 100 F, R 1 = 10 k , R 2 = 50 k , R 3 = 100 k . Find the equivalent series circuit of unknown impedance. 30

Schering Bridge Used for the precision measurement of capacitors and their insulating properties. C 3 is low loss (for general measurement) or having a very stable value and very small electric field (for insulating measurement). 31

Cont’… The condition for balance of the bridge 32

Cont’… The dissipation factor of a series RC, Indicate quality factor of capacitor 33

Example 6 An AC bridge has constants; C 3 = 0. 5 F, R 1 = 1 k parallel with C 1 = 0. 5 F, R 2 = 2 k. Find the unknown impedance and dissipation factor. 34

Wien Bridge Measure frequency of the voltage source using series RC in one arm and parallel RC in the adjoining arm. At balance point, 35

Cont’… The equivalent parallel of unknown impedance The equivalent series of unknown impedance 36

Cont’… In most, Wien Bridge, R 1 = R 3 and C 1 = C 3 37

Example 7 Find the equivalent parallel resistance and capacitance Rx and Cx in a Wien bridge at balance when f=2. 5 k. Hz, R 1=3. 1 k , R 2=25 k , C 1=5. 2μF, R 4=100 k. 38

AC Bridge for Inductance Measurement 39

Measurement of Inductance AC ◦ ◦ Bridge Comparison Bridge Maxwell Bridge Hay Bridge Owen Bridge 40

Comparison Bridge Measure an unknown inductance by comparing it with a known inductance. At balance, 41

Maxwell Bridge Measure an unknown inductance in terms of a known capacitance. At balance, 42

Example A Maxwell bridge is used to measure an inductive impedance. The bridge constants at balance are C 1 = 0. 01 F, R 1 = 470 k , R 2 = 5. 1 k , R 3 = 100 k . Find the equivalent series circuit of unknown resistance and inductance. Solution 43

Hay Bridge Measure an unknown inductance in terms of a known capacitance. R 1 series with C 1 44

Cont’… At balance Solve the equations (1) and (2) simultaneously 45

Cont’… Hay’s bridge measure the inductance in the range 1μH -100 H with ± 2% error. Best for measurement of inductance with high Q (>10) Requires very low value of R 1 to measure high Q inductance. 46

Owen Bridge Used for measuring an unknown inductance by balancing the loads of its four arms, one of which contains the unknown inductance. At balance, 47

Wien Bridge Measure frequency of the voltage source using series RC in one arm and parallel RC in the adjoining arm. At balance point, 48

The equivalent parallel of unknown impedance The equivalent series of unknown impedance 49

In most, Wien Bridge, R 1 = R 3 and C 1 = C 3 50

Example Find the equivalent parallel resistance and capacitance Rx and Cx in a Wien bridge at balance when f=2. 5 k. Hz, R 1=3. 1 k , R 2=25 k , C 1=5. 2μF, R 4=100 k. Solution 51

10 Q & Chapter 4 52