1. CHAPTER 5
DC AND AC BRIDGE
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NURJULIANA JUHARI

2. INTRODUCTION
DC & AC Bridge are used to measure resistance, inductance, capacitance and impedance.
Operate on a null indication principle. This means the indication is independent of the calibration of the indicating device or any characteristics of it.
Very high degrees of accuracy can be achieved using the bridges
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3. Types of bridges Two types of bridge are used in measurement:
1) DC bridge:
a) Wheatstone Bridge
b) Kelvin Bridge
2) AC bridge:
a) Similar Angle Bridge
b) Opposite Angle Bridge/Hay Bridge
c) Maxwell Bridge
d) Wein Bridge
e) Radio Frequency Bridge
f) Schering Bridge
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4. DIRECT - CURRENT (DC) BRIDGE
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5. a) WHEATSTONE BRIDGE
Defination: Consists of two parallel resistance branches with each branch containing two series elements.
Used for accurate measurements of resistance A B C D
Figure 5.1: Wheatstone Bridge Circuit
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6. OPERATION
The dc source, E is connected across the resistance network to provide a source of current through the resistance network
null detector usually a galvanometer is connected between the parallel branches (C-D) to detect a condition of balance.
No current, galvanometer= O pointer scale, have current- pointer scale deflect
Current flows and divides into the two arms at point A, ie I1 and I2
Bridge is balance when no current through the galvanometer or when the potential difference at points C & D is equal, potential across the galvanometer is zero.
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7. At balance the voltage across R1 and R2 also equal, therefore
Lets say to measured R4, vary the remaining resistors until the current through the null detector decrease to zero.
Then bridge is in balance condition, means voltage drop across R3 and R4 is equal
We can say that,
I3R3= I4R4 (1)
At balance the voltage across R1 and R2 also equal, therefore
I1R1=I2R2 (2)
No current flows through galvanometer G when the bridge is balance
I1 = I3 and I2=I4 (3)
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8. Cont… Substitute (3) in Eq (1), I1R3 = I2R4 (4) Eq (2) devide Eq (3)
R1/R3 = R2/R4
Then rewritten as
R1R4 = R2R3
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9. Example 1
Figure 5.2
Find Rx?
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10. Sensitivity of the Wheatstone Bridge
When the bridge is in an unbalanced condition, current flows through the galvanometer, causing a deflection of its pointer. The amount of deflection is a function of the sensitivity of the galvanometer.
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11. Cont..
Deflection may be expressed in linear or angular units of measure, and sensitivity can be expressed:
TOTAL DEFLECTION,
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12. Unbalanced Wheatstone Bridge
- Interest to measure current through the galvanometer
Used Thevenin’s theorem
Appling the voltage divider equation at point a n b
Vth= Va-Vb
Fig. 5-3: Unbalanced Wheatstone Bridge
Vth = Va-Vb
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13. Rb is internal resistance Assumed voltage source is low, so Rb = 0 Ω
We draw the bridge as shown in Figure 5-3
Therefore, the equivalent resistance thevenin is:
Fig. 5-4:
Thevenin’s resistance
Rth = R1//R3 + R2//R4
= R1R3/(R1 + R3) + R2R4(R2+R4)
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14. Thevenin’s Equivalent Circuit
Figure 5.5 : Thevenin’s Equivalent circuit
If a galvanometer is connected to terminal a and b, the deflection current in the galvanometer is
where Rg = the internal resistance in the galvanometer
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15. Example 2 R2 = 1.5 kΩ R1 = 1.5 kΩ Rg = 150 Ω E= 6 V R3 = 3 kΩ
Figure 5.6 : Unbalance Wheatstone Bridge
Calculate the current through the galvanometer ?
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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. Consider the circuit in Fig- 5.7
Figure 5.7 : Wheatstone Bridge with three equal arms
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17. Cont… The voltage at point a is given as The voltage at point b
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18. Cont.. Thevenin’s equivalent voltage is the difference in this voltage
If ∆r is 5% of R or less, Thevenin equivalent voltage can simplifies to
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19. Cont..
Thevenin equivalent resistance, when ∆r is small compared to R, therefore OR
We can draw the Thevenin equivalent circuit as shown in Figure 5.8
Figure 5.8: Approximate Thevenin’s equivalent circuit for a Wheatstone bridge containing three equal resistors and a fourth resistor differing by 5% or less
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20. b) KELVIN BRIDGE
is a modified version of the Wheatstone bridge. The purpose of the modification is to eliminate the effects of contact and lead resistance when measuring unknown low resistances.
Used to measure values of resistance below 1 Ω .
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21. Fig. 5-9: Basic Kelvin Bridge showing a second set of ratio arms
The resistor Rlc shown in figure represents the lead and contact resistance present in the Wheatstone bridge. The second set of ratio arms (Ra and Rb in figure) compensates
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22. Cont..
It can be shown that, when a null exists, the value for Rx is the same as that for the Wheatstone bridge, which is
for this relatively low lead contact resistance. At balance
the ratio of Ra to Rb must be equal to the ratio of R1 to R3.
Therefore when a Kelvin Bridge is balanced
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23. ALTERNATING – CURRENT (AC) BRIDGES
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24. INTRODUCTION AC BRIDGE
AC bridges are used to measure inductance and capacitances and all ac bridge circuits are based on the Wheatstone bridge. The general ac bridge circuit consists of 4 impedances, an ac voltage source, and detector as shown in Figure below. In ac bridge circuit, the impedances can be either pure resistance or complex impedances.
Fig 5.10 : General AC bridge circuit
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25. Fig. 5-11: Equivalent of balanced ac bridge circuit
Cont..
The operation of the bridge depends on the fact that when certain specific circuit conditions apply, the detector current comes zero. This is known as the null or balanced condition. Since the zero current means that are is no voltage difference across detector.
Fig. 5-11: Equivalent of balanced ac bridge circuit
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26. equation (1) divide by equation (2) Which also can written as
Cont....
The voltages from point a to point b and point a o point c must be equal
I1Z1 = I2Z (1)
The voltages from point d to point b and point d to point c must also equal, therefore
I1Z3 = I2Z4 (2)
equation (1) divide by equation (2)
Which also can written as
…(3)
…(4)
Both magnitude and phase angle of each four impedance must satisfy equation (3) and (4) for there to be a null or balance condition.
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27. Definition of electrical impedance
The impedance of a circuit element is defined as the ratio of the phasor voltage across the element to the phasor current through the element:
It should be noted that although Z is the ratio of two phasors, Z is not itself a phasor. That is, Z is not associated with some sinusoidal function of time.
For DC circuits, the resistance is defined by Ohm's law to be the ratio of the DC voltage across the resistor to the DC current through the resistor:
where the VR and IR above are DC (constant real) values
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28. Definition of Reactance, X
Reactance is the imaginary part of impedance, and is caused by the presence of inductors or capacitors in the circuit. Reactance is denoted by the symbol X and is measured in ohms.
A resistor's impedance is R (its resistance) and
its reactance, XR is 0.
A capacitance impedance:
XC = -1/ωC = -1/(2 πfC)
An inductive impedance:
XL = ωL = 2πfL
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29. a) Similar Angle Bridge
The similar angle bridge (refer figure below) is used to measure the impedance of a capacitive circuit. This bridge is sometimes called the capacitance comparison bridge of the series resistance capacitance bridge.
Fig 5-12 : Similar angle bridge
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30. The impedance of the arms Z1 = R1 Z2 = R2 Z3 = R3- jXc3 Z4 = Rx -jXcx
Used equation Z1Z4 = Z2Z (1)
Real terms and imaginary on each side must be equal
R1Rx=R2R3 (2)
-jR1Xcx = -jR2X (3)
From Eq 2 we get
Solve Eq 2 and Eq 4
……(5)
R1C3 = R2Cx (4)
….. (6)
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31. • to determine an unknown inductance with capacitance standard
b) Maxwell Bridge
• to determine an unknown inductance with capacitance standard
Fig 5-13 : Maxwell Bridge
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32. The impedance of the arms
Z1=1/(1/R1 + jwC1) Z2 = R2
Z3 = R3 Z4= Rx + jXLx
Used equation Z1Z4 = Z2Z (1)
Setting both imaginary and real parts equal to zero, we get
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33. c) Opposite Angle Bridge
The Opposite Angle Bridge or Hay Bridge (see Figure below) is used to measure the resistance and inductance of coils in which the resistance is small fraction of the reactance XL, that is a coil having a high Q, meaning a Q greater than 10.
Fig 5-14: Opposite angle bridge
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34. d) Wien Bridge
The Wein Bridge shown in Figure below has a series RC combination in one arm and a parallel combination in the adjoining arm. It is designed to measure frequency (extensively as a feedback arrangement for a circuit). It can also be used for the measurement of an unknown capacitor with great accuracy
Fig 5-15: Wein Bridge
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35. Equivalent parallel components
Equivalent series components
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36. e) Schering Bridge
used for the precession measurement of capacitors and their insulating properties for phase angle is nearly 90o.
Fig 5-16: Schering bridge
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37. Equating the real and imaginary terms, we find that
Impedance of the arms
Equating the real and imaginary terms, we find that
Z1= 1/(1/R1 + 1/-jXc1) Z2= R2
Z3= -jXC3 Z4= Rx -jXX
Substituting to the general equation gives
balance equation
And expanding
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38. LAST CHAPTER TRANSDUCER
NEXT WEEK..
LAST CHAPTER TRANSDUCER
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