DC & AC BRIDGES Part 1 (DC bridge). Objectives Ability to explain operation of Wheatstone Bridge and Kelvin Bridge. Ability to solve the Thevenin’s equivalent.

DC & AC BRIDGESPart 1 (DC bridge)

Objectives

• Ability to explain operation of Wheatstone Bridge and Kelvin Bridge.

• Ability to solve the Thevenin’s equivalent circuit for an unbalance Wheatstone Bridge.

• Define terms null or balance.

• Define sensitivity of Wheatstone bridge.

IntroductionDC & 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

Types of bridgesTwo types of bridge are used in measurement:

1) DC bridge:a) Wheatstone Bridgeb) Kelvin Bridge

2) AC bridge:a) Similar Angle Bridgeb) Opposite Angle Bridge/Hay Bridgec) Maxwell Bridged) Wein Bridgee) Radio Frequency Bridgef) Schering Bridge

DC BRIDGES

The Wheatstone BridgeThe Kelvin Bridge

Wheatstone BridgeA Wheatstone bridge is a measuring

instrument invented by Samuel Hunter Christie (British scientist & mathematician) in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. It is 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 except that in potentiometer circuits the meter used is a sensitive galvanometer.

Sir Charles Wheatstone (1802 – 1875)

Wheatstone Bridge

Basic dc bridge used for accurate measurement of resistance:

1

324 R

RRR

Fig. 5.1: Wheatstone bridge circuit

3241 RRRR

Definition: Basic circuit configuration consists of two parallel resistance branches with each branch containing two series elements (resistors). To measure instruments or control instruments

How a Wheatstone Bridge works?

• The dc source, E is connected across the resistance network to provide a source of current through the resistance network.

• The sensitive current indicating meter or null detector usually a galvanometer is connected between the parallel branches to detect a condition of balance.

• When there is no current through the meter, the galvanometer pointer rests at 0 (midscale).

• Current in one direction causes the pointer to deflect on one side and current in the opposite direction to otherwise.

• The bridge is balanced when there is no current through the galvanometer or the potential across the galvanometer is zero.

Cont.At balance condition;

2211 RIRI (1)

Voltage drop across R3 and R4 is equal

I3R3= I4R4 (2)

No current flows through galvanometer G when the bridge is balance, therefore:

I1 = I3 and I2=I4

(3)

voltage across R1 and R2 also equal, therefore

Cont.Substitute (3) in Eq (2),

I1R3 = I2R4 (4)

Eq (4) devide Eq (1)

R1/R3 = R2/R4

Then rewritten as

R1R4 = R2R3 (5)

Example 5-1Figure 5.2 consists of the following, R1 = 12k, R2 = 15 k, R3 = 32 k. Find the unknown resistance Rx. Assume a null exists(current through the galvanometer is zero).

Fig. 5-2: Circuit For example 5-1

Solution 5-1

RxR1 = R2R3

Rx = R2R3/R1 = (15 x 32)/12 k, Rx = 40 k

Sensitivity of the Wheatstone Bridge

When the bridge is in 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.

Cont.

A

radians

A

degrees

A

milimeters

S

Deflection may be expressed in linear or angular units of measure, and sensitivity can be expressed:

Total deflection, ISD

Unbalanced Wheatstone Bridge

Vth = Eab

42

4

31

3ab RR

R

RR

REE

Rth = R1//R3 + R2//R4

= R1R3/(R1 + R3)

+ R2R4(R2+R4)

Fig. 5-3: Unbalanced Wheatstone BridgeFig. 5-4: Thevenin’s resistance

Thévenin’s Theorem An analytical tool used to extensively analyze an unbalance bridge.

Thévenin's theorem for electrical networks states that any combination of voltage 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 the theorem can also be applied to general impedances, not just resistors. The theorem was first discovered by German physicist Hermann von Helmholtz in 1853, but was then rediscovered in 1883 by French telegraph engineer Léon Charles Thévenin (1857-1926).

Hermann von Helmholtz (1821 – 1894) Léon Charles Thévenin (1857-1926) German Physicist

French Engineer

Thevenin’s Equivalent Circuit

If a galvanometer is connected to terminal a and b, the deflection current in the galvanometer is

gth

thg RR

VI

where Rg = the internal resistance in the galvanometer

Example 5-2

G

R2 = 1.5 kΩR1 = 1.5 kΩ

R3 = 3 kΩR4 = 7.8 kΩ

Rg = 150 ΩE= 6 V

Figure 5.5: Unbalance Wheatstone Bridge

Calculate the current through the galvanometer ?

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.

ErR

rE

rRR

rRVVV abth

242

1

ER

r

R

rEEth

44

Cont..To find Rth:

RRR

Rth 22

An approximate Thevenin’s equivalent circuit

Example 5-3

G10 V

500 Ω 525 Ω

500 Ω500 Ω

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

Kelvin Bridge

The 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 .

Fig. 5-6: Basic Kelvin Bridge showing a second set of ratio arms

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

1

32

R

RRRx

Therefore when a Kelvin Bridge is balanced

a

bx

R

R

R

R

R

R

1

3

2

Cont.

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 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

Fig. 5-6: Basic Kelvin Bridge showing a second set of ratio arms

Example 5-4If in Figure 5-6, the ratio of Ra and Rb is

1000, R1 is 5 and R1 =0.5R2. What is the value of Rx.

Solution

The resistance of Rx can be calculated by

using the equation,Rx/R2=R3/5=1/1000

Since R1=0.5R2, the value of R2 is calculated as

R2=R1/0.5=5/0.5=10

So, Rx=R2(1/1000)=10 x (1/1000)=0.01

• CONTINUE…AC BRIDGE