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BridgesDC Bridge & AC Bridge
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Wheatstone Bridge
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Consists of two parallel resistance branchesA voltage source is
connected across the resistance networkA null detector, usually a
galvanometer is connected between the parallel branches to detect a
balanced conditionR1 & R2= precision resistors (standard)
knownR3= adjustable resistor (precisely calibrated) - measuredR4 /
RX= unknown to be calculatedWheatstone Bridge
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Wheatstone Bridge
Initially, the bridge is in unbalanced condition;galvanometer
will give a reading (current flows through the galvanometerV2 VXR3
is carefully adjusted so that no current will flow through the
galvanometerIG = 0V2 = VXthe bridge is now in balanced
condition
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Wheatstone BridgeFrom the figure,
also,
In balanced condition, V2 = VS,hence, R1RX = R2R3
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Wheatstone Bridge
Example
A wheatstone bridge has R2 = 3.5 k, R3 = 5.51 k and R1 = 7
k.Calculate for RXDetermine the measurement range if R3 is adjusted
from 1 k - 8 k
Ans: (a) 2.755 k; (b) 500 - 4 k
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Unbalanced Condition of Wheatstone Bridge
Sometimes measurement error could occur due to insufficient
sensitivity of the null detector (galvanometer)Galvanometer current
will be calculatedTo determine whether or not the galvanometer has
the required sensitivity to detect an unbalance conditionInternal
resistance of the galvanometer will be taken in accountThis current
sensitivity can be calculated by converting the wheatstone bridge
to its Thevenin equivalent
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Kelvin Bridge
For the above circuit, ratio of r1/r2 is exactly the same as
R1/R2. Hence, the voltage drop across R is eliminated
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Kelvin BridgeWith Vg = 0 (balance condition),
-------------------------(1)
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Kelvin BridgeAlso,
-------------------------------(2)
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Kelvin Bridge(2) (1)
and r1/r2 = R1/R2 or r1/R1 = r2/R2hence,
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Applications of Wheatstone Bridge Varley Loop
Wheatstone bridge is also used extensively by telephone
companies and others to locate faults in cablesThe fault may be two
lines shorted together or a single line shorted to groundTest
method called a Varley loop, which uses a Wheatstone bridge, is
often used to overcome this problem
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Varley Loop
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Varley LoopAssume a fault occurs at x in the conductor
represented by resistance RbA spare conductor, represented by
resistance Ra, is connected to the shorted conductor at point YTo
locate the fault, first set switch S, to position aBalance the
bridge by adjusting R4 R1R4 = R3(Ra + Rb)Ra + Rb = R1R4/R3Now, set
switch S to position bBalance the bridge by adjusting R4R1(R4 + RX)
= R3(Ra + Rb RX)Solving for RX
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AC BridgeSame principle as Wheatstone bridge, but with ac source
impedances replace resistancesNull condition: Z1Z4 = Z2Z3 1 + 4 = 2
+ 3
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AC BridgeExample
Referring to the above bridge, BC branch consists of R = 450 ;
AB branch consists of R = 300 in series with C = 0.265 F; and DA
branch consists of R = 200 in series with L = 15.9 mH. Let
frequency = 1 kHz. Calculate for impedance in CD branch.
Ans: j150 @ L = 23.9 mH
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Scherings Bridge
Scherings bridge is used to measure capacitanceNote that
Schering and capacitor both contain the letter C
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Maxwells Bridge
Maxwells bridge is used to measure inductance
