Presented by,

K.V, Vinay Shreyas B.E, M.Tech,Asst. Prof., Dept. of E & E,

H.K.B.K. College of Engineering, Bengaluru.

MEASUREMENT OF

DC & AC BRIDGES

Visvesvaraya Technological University

COURSE LEARNING OBJECTIVE

• To inculcate the operation and calculation of dc bridges to measure low, medium and high resistances.

INTRODUCTION• Bridge Circuit is a null method, operates on the principle of comparison. That is a known (standard) value is adjusted until it is equal to the unknown value.

•The bridge is said to be balance when there is no current through the galvanometer or potential difference across the galvanometer is zero.

•The relationship between the component values of the 4 arms of the bridge at the balancing is called balancing equation or balancing condition.

•This equation gives the value of unknown component.

DC BRIDGES• The measurement of resistance are classified as,

i. Low Resistance: order 1Ω.Ex: resistance of armature windings of electrical machines,

series field winding of D.C machine, shunts and lead wires.

ii. Medium Resistance: order 1Ω to 0.1MΩ.Ex: Shunt field windings of D.C machine and multipliers.

iii. High Resistance: 0.1MΩ and upwards.Ex: insulation resistance of cables and wires.

Measurement of Medium Resistance

• The different methods used for the measurement of Medium resistances are:

1. Ammeter-Voltmeter method.

2. Substitution method.

3. Wheatstone bridge method.

4. Ohmmeter method.

Wheatstone Bridge

• It is the very important device used for the measurement of medium resistance.•Fig shows the model and circuit of Wheatstone Bridge.

Wheatstone Bridge

•It consist of four arms, consisting of resistances P, Q, R & S with a source of emf E and null detector G.

•The bridge is said to be balanced when there is no current through the galvanometer.

•To have zero current through the galvanometer the points b and d must be at the same potential.

•Thus potential across arm ab must be same as the potential across arm ad.

• For balanced bridge,We can write, I1P= I2 R--------------------(1)

As galvanometer current is zero I1 = IG + I3 (IG = 0) = I3

Similarly, I2 = IG + I4 = I4

Considering battery path under balanced condition E = I1P + I3Q = I1P + I1Q = I1 (P +Q)

Therefore, I1 = E / P +Q = I3 ---------------------------(3)

Similarly, E = I2R + I4S = I2R+ I2S = I2 (R +S)

Therefore, I2 = E/R +S = I4 ---------------------------(4)

Using equation (3) & (4) in equation (1)

------------(2)

P(R + S) = R(P + Q) PR + PS = PR + RQ PS = RQ------------------(6)

Therefore,

If the three of the resistances are known, the fourth resistance can be determined as using the above equation.

Sensitivity of the Bridge•When the bridge is balanced, the current through galvanometer is zero.•But when the bridge is not balanced current flows through the galvanometer causing deflection.•The amount of deflection depends on the sensitivity of the galvanometer.•The bridge sensitivity SB is defined as the deflection of the galvanometer per unit fractional change in unknown resistance.•Bridge sensitivity ----------------(A)

∆R/R -------- unit fractional change in unknown resistance.

It can also be defined as amount of deflection per unit voltage across the galvanometer. This is also called as voltage sensitivity.

-----(B) θ--- deflection of galvanometerE--- voltage across galvanometer

Wheatstone Bridge under Un- balance

•Let the resistance R is changed to R+ΔR creating an unbalance.

•Because of this emf ‘e’ appear across the galvanometer branch.

•To obtain this, remove the branch of galvanometer and obtain the voltage across the open circuit terminals.

Wheatstone Bridge under Un- balance

EAB = I1P =

EAD = I2(R+ΔR) =

Therefore, VBD = VTH = VAD – VAB

Or EBD = VTH = EAD – EAB =

We know that,

Therefore, VTH = =

Wheatstone Bridge under Un- balance

=

=

R is very small. Therefore, R(R+S)<<(R+S)Δ Δ 2 S

VTH ≈ ≈ e

Now and the galvanometer sensitivity

Also,

Therefore, Finally,

Wheatstone Bridge under Un- balance

•From the above equation, sensitivity of the bridge depends on bridge voltage, bridge parameters and voltage sensitivity of the galvanometer.•Rearranging the above equation

•For a bridge, P = Q = R = S•Therefore, (Maximum Sensitivity)

Galvanometer Current

• The current through the galvanometer can be found by finding the Thevenin’s equivalent circuit for the bridge shown.

• The open circuit voltage between the Points b and d is

The Thevenin’s equivalent resistance is Found by short circuiting the voltage Source E and finding the resistance Between the points b and,

Where P and Q are in parallel, Similarly R and S is inparallel.

Galvanometer Current• Therefore,

• The current through the galvanometer is given By Ig (Rg + RTH) = VTH

Also Ig = VTH / (Rg + RTH)

We know that for a small change in resistance i.e., R + ∆RBridge sensitivity is

Here if P = Q = R = S then,

Therefore,

Limitation of Wheatstone Bridge•Wheatstone bridge is ideally used for the measurement of the Medium resistances but if it’s used for the measurement of low and high resistance the following are the limitations.

1. Resistance of Leads and contact resistance: the effect of lead resistance and contact resistance is very much significant while measuring low resistance.

A 22 SWG has 0.012 ohm and 4 dial resistance box has 0.01 ohm.

2. When high resistance are measured the resistance of the bridge becomes so large that the galvanometer becomes insensitive.

3. Thermoelectric e.m.f’s are present in the circuit and they affect the galvanometer deflection.

4. The excessive currents may generate heat which may cause the permanent change in the resistance.