Schering Bridge :
Let C1 and r2 are the unknown quantities
C2 = a standard capacitor
C4 = a variable capacitor
R3 = a non-inductive resistance
R4 = a variable non-inductive resistance
At balance condition,
Equating real part we get,
Equating imaginary part we get,
∴ Dissipation Factor = D1 = ωC1r1 = ωC 4R 4
AC bridges through which frequency can be measured :
1. Wien’s Bridge
Wien’s Bridge :
At balance condition, Zab . Zcd = Zad . Zbc
Equating real part we get,
Equating imaginary part wet get,
In most of the Wien’s bridges, R1 = R2 = R and C1 = C2 = C
then, equation becomes,
R4 = 2R3
and equation becomes,
Measurement of Resistance :
Classification of resistance
Low resistance ⇒ R < 1Ω
Medium resistance ⇒ 1Ω < R < 0.1M Ω
High resistance ⇒ R > 0.1 M Ω
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
Ammeter connected near the load:
Let Ra be the resistance of the ammeter.
∴ Voltage across the ammeter , Va = IRa
Now measured value of resistance,
∴ True value of resistance,
R = Rm1 - Ra
Ammeter voltmeter method
I = IR + IV
Let RV be the resistance of the voltmeter.
∴ Current through the voltmeter.
Iv = V/Rv
Measured value of resistance,
Now, true value of resistance is:
or, RV >> Rm2, and therefore Rm2/ Rv is very small.
Now equation may be written as,
By binomial theorem,
⇒Thus the measured value of resistance is smaller than the true value.
Note: ⇒ This method is used when measuring low resistance values.
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.
where, θ1 = the deflection with standard resistor.
θ2 = the deflection with unknown resistor in circuit.
G is the galvanometer.
Wheatstone Bridge Method :
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
I1P = I2R
I1 / I2 = R/P
for the galvanometer current to be zero, The following conditions also exist:
where, E = emf of the battery. From the equation;
Carey-Foster Slide-wire Bridge : This method is used for the purpose of determining the difference between the standard and the unknown resistances.
• Exact balance is obtained by adjustment of the sliding contact on the ide-wire.
Let l1 be the distance of the sliding contact from the left-hand end of the slide wire. The resistances R and S are then inter-changed and balance is again obtained. Let the distance now be l2.
Ist case : For the Ist balance,
Where r is the resistance per unit length of the slide wire.
IInd case : For the 2nd balance,
where L is length being included between R and S.
Now, from equation
• Ohm-meter method is used for measuring resistance of field coils of machines.
• It is used for measurement of heating element resistance.
• It is also used in measuring and sorting of resistors.
Measurement of Low Resistance :
• Construction : These are provided with four terminal to eliminate the effect of contact resistance. Out of four terminals, two terminals are used for current injection, these are current terminals and remaining two terminals are used for measurement of potential dropped across the resistances. These terminals are called voltage terminals.
Here, I1 and I2 are current terminals V1 and V2 are voltage terminals.
Methods for measurement of low resistance
• Ammeter-voltmeter method.
• Kelvin’s double bridge method.
• Potentiometer method
⇒ Ammeter-voltmeter methods are already discussed in this chapter previously.
Kelvin’s Double Bridge Method for Measurement of Low Resistances :
• The Kelvin’s bridge is a modification of the Wheatstone bridge and provides greatly increased accuracy in measurement of low value resistances.
• The Kelvin’s bridge arrangement are given in figure below,
• The first set of ratio arms is P and Q. The second set is of ratio arms, P and q which is used to connect the galvanometer to point d at the appropriate potential between points m and n to eliminate the effect of connecting lead of resistance r between the known resistance, R and standard resistance S.
• The ratio p/q is made equal to P/Q. Under balance conditions there is no-current through the galvanometer, the voltage drop between a and b i.e. Eab is equal to voltage drop Eamd between a and c.
for zero galvanometer deflection, Eab = Eamd
⇒ This equation shows the usual working equation for the Kelvin bridge.
⇒ It indicates that the resistance of connecting lead, r1 has no-effect on the measurement, provided that the two sets of ratio arms has equal ratios.
Potentiometer Method :
• This method is a comparison type method. Measurement using comparison methods are capable of a high degree of accuracy because the result obtained does not depend upon on the actual deflection of a pointer, as is the case in deflectional methods, but only upon the accuracy with which the voltage of the reference source is known.
Measurement of High Resistance :
• The different methods employed are :
• High resistance of the order of hundreds or thousands of megaohm are often encountered in electrical equipment, and frequently must be measured.
• Common examples are :
Difficulties in Measuring High Resistances :
• Error due to leakage current.
• Error due to electrostatic effect or charges are gathered.
• Error due to capacitive effect.
⇒ Problem of leakage current can be eliminated by using guard circuit.
⇒ In loss of charge method, on the principle of discharging of capacitor through unknown resistance, for high resistance value.
⇒ Meggar method is used for measurement of insulation resistance and earth resistance.