Chapter 1 (Part 2) AC Bridges
AC bridges through which frequency can be measured : 1. Wein’s Bridge v Wein’s Bridge : It is primarily well known as a frequency determining bridge. It ma y be emp loyed in a “Harm onic distortion analyzer” where it is used as “Notch filter”. There also finds applications in Audio and High frequency oscillators as the frequency determining device (100 Hz-100 KHz).
At balance condition, Zab . Zcd = Zad . Zbc
Equating real part we get,
Equating imaginary part wet get,
In most of the Wein’s bridges, R1 = R2 = R
and C1 = C2 = C then, equation becomes,
R = 2R
and equation becomes,
The bridge may be used in “Frequencydetermining device” balanced by a single control and this control may be calibrated directly in terms of frequency. It may also be used for the measurement of “Capacitance”.
Measurement of Resistance : Classification of resistance Low resistance Þ R < 1W Medium resistance Þ 1W< R < 0.1M W High resistance Þ R > 0.1 M W Measurement of Medium Resistance The different Methods used for measurement of medium resistance are: (i) Voltmeter-Ammeter method (ii) Substitution method (iii) Wheatstone bridge method (iv) Ohmeter method Voltmeter-Ammeter Method: This method is very popular since the instruments required for this test are usually available in the laboratory. Measured value of resistance is given by
Ammeter connected near the load
Let Ra be the resistance of the ammeter QVoltage across the ammeter , VVa = IRa Now measured value of resistance,
= R + Ra \ True value of resistance,
Thus the measured value of resistance is higher the value. It is also clear from above that the true value is equal to measured value only when the ammeter resistance, Ra is zero. \ Relative error ( Î r ) =
It is clear from equation (4.40) that the error in measurements would be small if the value of resistance under measurement is large as compared to the internal resistance of the ammeter. So the type of circuit should be us ed when measuring high resistance values.
Ammeter voltmeter method Voltmeter connected near the load
In this circuit the voltmeter measures the true value of voltage but the ammeter measures the sum of currents through the resistance R and the voltmeter V.
I = IR + IV
Let RV be the resistance of the voltmeter. \ Current through the voltmeter.
Measured value of resistance,
Now, true value of resistance is
From this equation, it is clear that the true value of resistance is the measured value only if the resistance of voltmeter Rv, is infinite however, if the resistance of voltmeter is very large as compared to the resistance under measurement.
or, RV >> Rm2, and therefore RmV2 R
is very small.
Now equation may be written as,
By binomial theorem,
Þ Thus the measured value of resistance is smaller than the true value. \ Relative error
Rm2@ R \ then relative error is,
Note: Þ This method is used when measuring low resistance values. ¦ Substitution Method : Substitution method is more accurate method than the ammeter voltmeter method, as it is not subject to the errors encountered in this method.
Let, R = unknown resistance S = standard variable resistance r = regulating resistance and there is a switch for putting R and S into the circuit alternately.
n Operation The switch is put at position 1, and resistance R is connected in the circuit. The regulating resistance r is adjusted till the ammeter pointer is at a chosen scale mark. Now the switch is thrown to position. 2 Putting the standard variable resistance S in the circuit.
The value of S is varied till the same deflection, as was obtained with R in the circuit, is obtained. The settings of the dials of S are read. Thus the value of unknown resistance R is equal to the dial settings of resistace S,
where, q1 = the deflection with standard resistor and q2 = the deflection with unknown resistor in circuit. and G is the galvanometer. ¦ Wheatstone Bridge Method : The wheatstone bridge is an instrument for making comparision measurements and operates upon a null deflection principle. A very important device used in the measurement of medium resistance is the wheatsone bridge. It is highly accurate and reliable instruments, because the indication is independent of the calibration of the null indicating instrument or any of its characteristics.
This method is extensively used in industries.
where, R is the unknown resistance.
S is called the ‘standard arm’ or known resistance of the bridge and P and Q are called the ratio arms for bridge balance, we can write
for the galvonometer current to be zero, The following conditions also exist
where, E = emf of the battery. from the equation