SHROFF S.R. ROTARY INSTITUTE OF CHEMICAL TECHNOLOGY Principal Supporter & Sponsor- United Phosphorous Limited(UPL)/ Shroff Family Managed By Ankleshwar Rotary Education Society Approved by AICTE, New Delhi , Govt. of Gujarat & GTU Affiliated

AC BRIDGES

7.1 Introduction to AC Bridge. AC bridges are used to measure inductance and capacitance. All the AC bridges are based on the Wheatstone bridge. In the AC bridge the bridge circuit consists of four impedances and an ac voltage source. The impedances can either be pure resistance or complex impedance. Other than measurement of unknown impedance, AC bridge are commonly used for shifting phase.

Figure 7.2: Equivalent of Balance (nulled) AC Bridge. Cont’d… Operation of AC Bridge: When the specific circuit conditions apply, the detector current becomes zero, which is known as null or balance condition. Since zero current, it means that there is no voltage difference across the detector, Figure 7.2. Voltage at point b and c are equal. The same thing at point d. From two above equation yield general bridge equation; Figure 7.2: Equivalent of Balance (nulled) AC Bridge.

Figure 7.3: (a) and (b) are Simple AC Bridge Circuit. Cont’d… Figure 7. 3(a) and 7.3 (b) is a simple AC Bridge circuit. Figure 7.3: (a) and (b) are Simple AC Bridge Circuit.

7.5 Wein Bridge The Wein Bridge is versatile where it can measure either the equivalent –series components or the equivalent-parallel components of an impedance, Figure 7.8. This bridge is used extensively as a feedback for the Wein bridge oscillator circuit. Figure 7.8: Wein Bridge.

Schering bridge It is used extensively for the measurment of capacitors. It is also useful for measuring insulating properties i.e. phase angles very nearly fig. shows basic circuit arrengement. One of the ratio are consists of a resistance in parrallel with a capacitor and standard arm consists only a capacitor. The standard capacitor is high quality mica capacitor or an air capacitor for insulation measurement . The general bridge balance equation is ,

Substituting , Separating real and imaginary terms ,The equation gives the value Of unknown capacitance Cx inTerms of standard capacitorC3 , R1 ,anR2 . The bridge can be used to define the quality Of capacitor by obtaining

Power factor : it is defined as the cosine of the phase angle of the circuit . p.f. = for phase angles close to , the reactance is equal to impedance. P.f. = Dissipation factor : it is defined as the cotangent of the phase angle.

The quality of a coil is define as The quality of a coil is define as . The dissipation factor is the reciprocal of quality factor . Putting values of Rx and Cx .

If R1 is fixed then C1 may be calibrated to give dissipation D i. e If R1 is fixed then C1 may be calibrated to give dissipation D i.e. quality of capacitor . The calibration of C1 is good only for particular frequency , as Ѡ term is present in the equation . Commercial schering bridge measures capacitors from 100 pf -1 F with accuracy . The bridge is widely used for testing small capacitors at low voltages with high precision .

The Anderson’s Bridge is a modification of the Maxwell’s inductance capacitance bridge. In this method, the self-inductance is measured in terms of a standard capacitor. This method is applicable for precise measurement of self-inductance over a very wide range of values.

The connection of the bridge for balanced condition is shown below:-

The phasor diagram of the bridge for balanced condition is given below:-

Let, L1= self-inductance to be measured R1= resistance of self-inductor r1= resistance connected in series with self-inductor R, R2, R3, R4= known non-inductive resistances C= fixed standard capacitor At balance, I1=I3 & I2=Ic+I4, Now,

Writing the other balance equations And, Substituting the value of Ic in the above equations we have, Or, ……..(1) Writing the other balance equations

And, Or, ……………(2) From equations (1) & (2) we obtain, Equating the real & imaginary parts,

ADVANTAGES:- A fixed capacitor can be used instead of a variable capacitor as in the case of Maxwell’s bridge. This bridge may be used for accurate determination of capacitor in terms of inductance.

DISADVANTAGES:- The Anderson’s bridge is more complex than its prototype Maxwell’s bridge .The Anderson’s bridge has more parts and is more complicated to set up and manipulate. The balance equations are not simple and in facts are much more tedious. An additional junction point increases the difficulty of shielding the bridge.

MAXWELL’S BRIDGE The Maxwell’s bridge measures an unknown inductance in terms of a known capacitance. One of the ratio arms has a resistance and capacitance in parallel. we know that the general equation of bridge balance is,

Z1 ZX = Z2 Z3 ZX = Z2 Z3 * 1/Z1 =Z2 Z3 Y1 Here, Y1=Admittance of arm 1 Z2 = R2 Z3 = R3 Y1 = 1/R1 + jωC1 Substituting these values, Zx = Rx + jωLx = R2 R3 ( 1/R1 + jωC1) Zx = R2 R3/R1 + jωR2 R3 C1

Q = ωLx/Rx = ωR2 R3 C1/(R2 R3 /R1) Separating real and imaginary parts, Rx = R2 R3/R1 Lx = R2 R3 C1 To obtain bridge balance, first R3 is adjusted for inductive balance and R1 is adjusted for resistive balance. The quality factor of the coil is given by, Q = ωLx/Rx = ωR2 R3 C1/(R2 R3 /R1) Q = ω R1 C1

Advantages The balance equation is independent of frequency. The two balance equation are independent. The scale of resistance can be calibrated to read the inductance and Q value. It is useful for measurement of wide range of inductance at power and audio frequencies.

Disadvantages It cannot be used for measurement of high Q values. it is limited to measure low Q values (1<Q>10) It cannot be used for measurement of very low Q values ,because of balance converge problem. Commercial Maxwell’s bridge measures the inductance from 1-100H , with ± 2% error.

Hay Bridge Used to measure the L and R of an inductor having a small series resistance

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