4.1 General form of
A.C. Bridge
AC bridge are similar to D.C. bridge in topology(way of connecting).It consists of four arm AB,BC,CD and DA .Generally the impedance to be measured is connected between ‘A’ and ‘B’. A detector is connected between ‘B’ and ’D’. The detector is used as null deflection instrument. Some of the arms are variable element. By varying these elements, the potential values at ‘B’ and ‘D’ can be made equal. This is called balancing of the bridge.
At the balance condition, the current through detector is zero.
At balance condition,
Voltage drop across ‘AB’=voltage drop across ‘AD’.
From equation -2.1, it can be seen that, equation -2.4 and equation-2.5 are equal.
∗ For balance condition, magnitude on either side must be equal.
∗ Angle on either side must be equal.
Summary
For balance condition,
4.2 Types of detector
The following types of instruments are used as detector in A.C. Bridge.
• Vibration galvanometer
• Head phones (speaker)
• Tuned amplifier
4.2.1 Vibration
galvanometer
Between the point ‘B’ and ‘D’ a vibration galvanometer is connected to indicate the bridge balance condition. This A.C. galvanometer which works on the principle of resonance. The A.C. galvanometer shows a dot, if the bridge is unbalanced.
4.2.2 Head phones
Two speakers are connected in parallel in this system. If the bridge is unbalanced, the speaker produced more sound energy. If the bridge is balanced, the speaker do not produced any sound energy.
4.2.3 Tuned amplifier
If the bridge is unbalanced the output of tuned amplifier is high. If the bridge is balanced, output of amplifier is zero.
4.3 Measurements of
inductance
4.3.1 Maxwell’s
inductance bridge
The choke for which R1 and L1 have to measure connected between the points ‘A’ and ‘B’. In this method the unknown inductance is measured by comparing it with the standard inductance.
L2 is adjusted, until the detector indicates zero current.
Let R1= unknown resistance
L1= unknown inductance of the choke.
L2= known standard inductance
R1,R2,R4= known resistances.
Z 2 Z3=At balance condition, Z1 Z4
Advantages
Expression for R1 and L1 are
simple. Equations area simple
They do not depend on the frequency (as w is cancelled) R1 and L1 are independent of each other.
Disadvantages
Variable inductor is costly.
Variable inductor is bulky.
4.3.2 Maxwell’s
inductance capacitance bridge
Unknown inductance is measured by comparing it with standard capacitance. In this bridge, balance condition is achieved by varying ‘C4’.
At balance condition, Z1Z4=Z3Z2
Comparing real parts,
R1R4 = R2 R3
Advantages
Equation of L1 and R1 are simple
They are independent of frequency.
They are independent of each other.
Standard capacitor is much smaller in size than standard inductor.
Disadvantages
Standard variable capacitance is costly.
It can be used for measurements of Q-factor in the ranges of 1 to 10.
It cannot be used for measurements of choke with Q-factors more than 10.
We know that Q =wC4R4
For measuring chokes with higher value of Q-factor, the value of C4 and R4 should be higher. Higher values of standard resistance are very expensive. Therefore this bridge cannot be used for higher value of Q-factor measurements.
4.3.3 Hay’s bridge
Comparing the imaginary terms,
Advantages
Fixed capacitor is cheaper than variable capacitor.
This bridge is best suitable for measuring high value of Q-factor.
Disadvantages
Equations of L1and R1 are complicated.
Measurements of R1 and L1 require the value of frequency.
This bridge cannot be used for measuring low Q- factor.
4.3.4 Owen’s bridge
Advantages
Expression for R1 and L1 are simple.
R1 and L1 are independent of Frequency.
Disadvantages
The Circuits used two capacitors.
Variable capacitor is costly.
Q-factor range is restricted.
Advantages
Variable capacitor is not required.
Inductance can be measured accurately
R1 and L1 are independent of frequency.
Accuracy is better than other bridges.
Disadvantages
Expression for R1 and L1 are complicated.
This is not in the standard form A.C. bridge.
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