Unit - 2
Measurement Of Resistance
Q1) Describe the various methods of measurement of resistances?
A1) (1) Measurement of Low resistance: This method is used measure the resistance below 1Ω. Kelvin’s Double Bridge is used to measure small resistances.
(2) Measurement of Medium Resistance: This method is used to measure resistance ranging between 1-100 k Ω. Ammeter-Voltmeter Method & Wheatstone Bridge are the two methods in this category.
(3) Measurement of High Resistance: This method is used to measure resistance above 100k Ω. Megger is used to measure high value of resistance in a circuit.
Q2) Describe Sources & Detectors in AC Bridges?
A2) Sources: for low frequency measurement the power line supply act as source of excitation and for high frequency measurement the electronic oscillator is used as excitation voltage
Detectors:
- Headphones: It is used at frequency from 250 Hz to 3-4 kHz and is the most sensitive detector for this range.
- Vibration Galvanometer: It can be used from 5-1000 Hz and are useful in low AF and power.
- Tuneable Amplifier Detector: It can be used at 10 Hz to 100 kHz
- Cathode Ray Oscilloscope: It is used for higher frequency mainly above 5kHz.
Q3) Describe Wheatstone bridge method for measurement of Medium resistance?
A3) This is the simplest and the most basic bridge circuit used in measurement studies. It mainly consists of four arms of resistance P, Q; R and S. R is the unknown resistance under experiment, while S is a standard resistance. P and Q are known as the ratio arms. An EMF source is connected between points a and b while a galvanometer is connected between points c and d.
A bridge circuit always works on the principle of null detection, i.e. we vary a parameter until the detector shows zero and then use a mathematical relation to determine the unknown in terms of varying parameter and other constants. Here also the standard resistance, S is varied in order to obtain null deflection in the galvanometer. This null deflection implies no current from point c to d, which implies that potential of point c and d is same. Hence,
Also, 
and 
Combining the above two equation, we get
Q4) How is measurement of earth resistance is carried out?
A4) The measurement of earth resistance is made by the potential fall method. The resistance area of the earth electrode is the area of the soil around which a voltage gradient is measured with a commercial instrument. In the figure shown below E is the earth electrode under rest, and A is an auxiliary earth electrode positioned so that two resistance areas do not overlap. B is the second auxiliary electrode which is placed between E and A.
An alternating current of steady state value passes through the earth path from E to A and the voltage drop between E and B is measured.
The electrode B is moved from position B1 and B2 respectively so that the resistance area does not overlap. If the resistance values determined is of approximately the same in all three cases, the mean of the three readings can be taken as the earth resistance of the earth electrode.
The auxiliary earth electrode A must be driven in at a point further away from E and the above test repeated until the group of three readings obtained are in good agreement. The alternating current source is used to eliminate the electrolytic effect.
The test can be performed, with current at power frequency from a double wound transformer, using a voltmeter and an ammeter as shown in the figure above by mean of an earth tester.
Q5) Explain the principle of measurement of resistance using Kelvin’s Double Bridge?
A5) Kelvin’s double bridge is a modification of simple Wheatstone bridge. Figure below shows the circuit diagram of Kelvin’s double bridge.
As we can see in the above figure there are two sets of arms, one with resistances P and Q and other with resistances p and q. R is the unknown low resistance and S is a standard resistance. Here r represents the contact resistance between the unknown resistance and the standard resistance, whose effect we need to eliminate. For measurement we make the ratio P/Q equal to p/q and hence a balanced Wheatstone bridge is formed leading to null deflection in the galvanometer. Hence for a balanced bridge we can write:
Ead = Eamc
Where, 
Using the value of Eab in the above equation & solving it using P/Q=p/q, we get
Hence we see that by using balanced double arms we can eliminate the contact resistance completely and hence error due to it. To eliminate another error caused due to thermo-electric emf, we take another reading with battery connection reversed and finally take average of the two readings. This bridge is useful for resistances in range of 0.1µΩ to 1.0 Ω.
Q6) Explain the different parts of Megger/Megohmmeter?
A6) The megger is used very commonly for measurement of insulation resistance of electrical machines, insulators, bushings, etc. The traditional analog deflecting-type megger is essentially a permanent magnet crossed-coil shunt type ohmmeter.
Deflecting and Control coil: Connected parallel to the generator, mounted at right angle to each other and maintain polarities in such a way to produced torque in opposite direction.
Permanent Magnets: Produce magnetic field to deflect pointer with North-South pole magnet.
Pointer: One end of the pointer connected with coil another end deflects on scale from infinity to zero.
Scale: A scale is provided in front-top of the megger from range ‘zero’ to ‘infinity’; enable us to read the value.
D.C generator or Battery connection: Testing voltage is produced by hand operated DC generator for manual operated Megger. Battery / electronic voltage charger is provided for automatic type Megger for same purpose. Pressure Coil Resistance and Current Coil Resistance: Protect instrument from any damage because of low external electrical resistance under test.
Q7) Derive the equation for Maxwell’s Inductance bridge?
A7) This bridge measures the unknown value of inductance by comparison with a variable standard self inductance.
Let R1 & L1 are unknown quantity
L2 = Variable Inductance of fixed resistance ‘r2’
R2 = Variable Resistance connected in series with ‘L2’
R3 & R4 = Known Non-Inductive Resistances
At balance condition,
Equating real & imaginary part we get,
Q8) Describe the phasor diagram of Anderson’s Bridge?
A8) 
For balance condition,
[(
]*
=
Equating Real & Imaginary Part, we get
Q9) On a 250V supply a fault having resistance of 20 ohm develops between the unearthed end of winding of an electric heater & the frame. If the resistance of the substation is 5 ohm that of human body is 2000 ohm & the safe current is 25 mA, what is the safe maximum resistance of consumer’s earth electrode?
A9) Let R be the resistance of earth electrode at consumer end
Voltage drop across human body
V = 25*10-3*2000= 50V
Voltage between the points
=250-50= 200V
Current, I = 200/(20+5)= 8A
current through human body = I*(R/R+2000)= 25*10-3
Solving for R, we get
R= 6.27 ohm
Q10) Explain the torque equation of Megger?
A10) Work philosophy based on ohm-meter or ratio-meter. The deflection torque is produced with megger tester due to the magnetic field produced by voltage and current, similarly like ‘Ohm’s Law’.
The torque of the megger varies in a ration with V/I, (Ohm’s Law: - V = IR or R = V/I). Electrical resistance to be measured is connected across the generator and in series with deflecting coil.
Produced torque shall be in opposite direction if current supplied to the coil.
- High Resistance = No Current: - No current shall flow through deflecting coil, if resistance is very high i.e. infinity position of pointer.
- Small Resistance = High Current :- If circuit measures small resistance allows a high electric current to pass through deflecting coil, i.e. produced torque make the pointer to set at ‘ZERO’.
- Intermediate Resistance = Varied Current: - If measured resistance is intermediate, produced torque align or set the pointer between the range of ‘ZERO to INIFINITY’.
