1. CHAPTER 5
DC AND AC BRIDGES

2. 1. Introduction
Bridge circuits (DC & AC) are an instrument 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.
Used in control circuits.
# One arm of the bridge contains a resistive element
that is sensitive to the physical parameter
(temperature, pressure, etc.) being controlled.

3. 1. Introduction
TWO (2) TYPES of bridge circuits 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

4. DIRECT-CURRENT (DC)BRIDGE

5. Figure 5.1: Wheatstone Bridge Circuit
The Wheatstone bridge is an
electrical bridge circuit used
to measure resistance.
It consists of a voltage source
and a galvanometer that
connects two parallel branches,
containing four resistors.
Figure 5.1: Wheatstone Bridge Circuit
One parallel branch contains one known resistance and one
unknown; the other parallel branch contains resistors of known
resistances.

6. Figure 5.1: Wheatstone Bridge Circuit
In the circuit at right, R4 is the unknown resistance; R1, R2 and R3 are resistors of known resistance where the resistance of R3 is adjustable.
How to determine the resistance of the unknown resistor, R4?
“The resistances of the other three are adjusted and balanced until the current passing through the galvanometer decreases to zero”.
Figure 5.1: Wheatstone Bridge Circuit

7. Figure 5.1: Wheatstone Bridge Circuit
R3 is varied until voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer. A B C D
Figure 5.1: Wheatstone Bridge Circuit
Figure 5.2: A variable resistor; the amount of resistance between the connection terminals could be varied.

8. Figure 5.1: Wheatstone Bridge Circuit
When the bridge is in balance condition (no current flows through galvanometer G), we obtain;
voltage drop across R1 and R2 is
equal,
I1R1 = I2R2
voltage drop across R3 and R4 is
I3R3 = I4R4
Figure 5.1: Wheatstone Bridge Circuit

9. Figure 5.1: Wheatstone Bridge Circuit
In this point of balance, we also
obtain;
I1 = I3 and I2 = I4
Therefore, the ratio of two resistances in the known leg is equal to the ratio of the two in the unknown leg;
Figure 5.1: Wheatstone Bridge Circuit

10. 2. Wheatstone Bridge
Example 1
Figure 5.3
Find Rx?

11. 2. Wheatstone Bridge Sensitivity of the Wheatstone Bridge
When the pointer of a bridge galvanometer deflects to right or to left direction, this means that current is flowing through the galvanometer and the bridge is called in an unbalanced condition.
The amount of deflection is a function of the sensitivity of the galvanometer. For the same current, greater deflection of pointer indicates more sensitive a galvanometer.
Figure 5.4.

12. 2. Wheatstone Bridge Sensitivity of the Wheatstone Bridge (Cont…)
Sensitivity S can be expressed in units of:
How to find the current value?
Figure 5.4.

13. Fig. 5.5: Thevenin’s equivalent voltage
2. Wheatstone Bridge
Thevenin’s Theorem
Thevenin’s theorem is a approach used to determine the current flowing through the galvanometer.
Thevenin’s equivalent voltage is found by removing the galvanometer from the bridge circuit and computing the open-circuit voltage between terminals a and b.
Fig. 5.5: Thevenin’s equivalent voltage
Applying the voltage divider equation, we express the voltage at point a and b, respectively, as

14. Fig. 5.6: Thevenin’s resistance
2. Wheatstone Bridge
Thevenin’s Theorem (Cont…)
The difference in Va and Vb represents Thevenin’s equivalent voltage. That is,
Fig. 5.5: Wheatstone bridge with the galvanometer removed
Thevenin’s equivalent resistance is found by replacing the voltage source with its internal resistance, Rb. Since Rb is assumed to be very low (Rb ≈ 0 Ω), we can redraw the bridge as shown in Fig. 5.6 to facilitate computation of the equivalent resistance as follows:
Fig. 5.6: Thevenin’s resistance

15. 2. Wheatstone Bridge Thevenin’s Theorem (Cont…)
Fig. 5.6: Thevenin’s resistance
If the values of Thevenin’s equivalent voltage and resistance have been known, the Wheatstone bridge circuit in Fig. 5.5 can be changed with Thevenin’s equivalent circuit as shown in Fig. 5.7,
Fig. 5.5: Wheatstone bridge circuit
Fig. 5.7: Thevenin’s equivalent circuit

16. Fig. 5.7: Thevenin’s equivalent circuit
2. Wheatstone Bridge
Thevenin’s Theorem (Cont…)
If a galvanometer is connected to terminal a and b, the deflection current in the galvanometer is
Fig. 5.7: Thevenin’s equivalent circuit
where Rg = the internal resistance in the galvanometer

17. 2. Wheatstone Bridge Example 2 R2 = 1.5 kΩ R1 = 1.5 kΩ Rg = 150 Ω
E= 6 V
Figure 5.8 : Unbalance Wheatstone Bridge
Rg = 150 Ω
R3 = 3 kΩ
R4 = 7.8 kΩ
Calculate the current through the galvanometer ?

18. 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 develop an approximate but accurate expression for Thevenin’s equivalent voltage and resistance. Consider the circuit in Fig- 5.9, the voltage at point a is given as
The voltage at point b is expressed as
Figure 5.9: Wheatstone Bridge with three equal arms

19. 2. Wheatstone Bridge Slightly Unbalanced Wheatstone Bridge (Cont…)
Thevenin’s equivalent voltage is the difference in this voltage
If ∆r is 5% of R or less, Thevenin equivalent voltage can be simplified to be

20. Figure 5.10: Resistance of a Wheatstone.
2. Wheatstone Bridge
Slightly Unbalanced Wheatstone Bridge (Cont…)
Thevenin’s equivalent resistance can be calculated by replacing the voltage source with its internal resistance and redrawing the circuit as shown in Figure Thevenin’s equivalent resistance is now given as o R
R + Δr
If ∆r is small compared to R, the equation simplifies to or
Figure 5.10: Resistance of a Wheatstone.

21. 2. Wheatstone Bridge Slightly Unbalanced Wheatstone Bridge (Cont…)
We can draw the Thevenin equivalent circuit as shown in Figure 5.11
Figure 5.11: Approximate Thevenin’s equivalent circuit for a Wheatstone bridge containing three equal resistors and a fourth resistor differing by 5% or less

22. 3. Kelvin Bridge 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.
The measurement with a high
degree of accuracy can be done
using the Kelvin bridge for
resistors in the range of 1 Ω to
approximately 1 µΩ.
Fig. 5.12: Basic Kelvin Bridge showing a second set of ratio arms
Since the Kelvin bridge uses a second set of ratio arms (Ra and Rb, it is
sometimes referred to as the Kelvin double bridge.

23. 3. Kelvin Bridge
Fig. 5.12: Basic Kelvin Bridge showing a second set of ratio arms
The resistor Rlc represents the lead and contact resistance
present in the Wheatstone bridge.
The second set of ratio arms (Ra and Rb in figure) compensates
for this relatively low lead-contact resistance.

24. 3. Kelvin Bridge
When a null exists, the value for Rx is the same as that for the Wheatstone bridge, which is or
At balance the ratio of Rb to Ra must be equal to the ratio of R3 to R1. Therefore,