Thus to eliminate this issue small valued resistance are constructed with four terminals. Two terminals are current terminals and other two are potential terminals.
Figure below shows the construction of low resistance.
Low Resistance
The current is flown through current terminals C1 and C2 while the potential drop is measured across potential terminals V1 and V2. Hence we can find out the value of resistance under experiment in terms of V and I as indicated in the above figure. This method helps us to exclude the contact resistance due to current terminals and though contact resistance of potential terminals still comes into picture, it is very small fraction of high resistance potential circuit and hence induces negligible error.
The methods employed for measurement of low resistances are:-
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
Putting eqn 2 in 1 and solving and 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.
One of the coil called current coil, is connected to current terminals C1 and C2, while the other coil called, voltage coil is connected to potential terminals V1 and V2. Voltage coil carries current proportional of the voltage drop across R and so is its torque produced. Current coil carries current proportional to the current flowing through R and so is its torque too. Both the torque acts in opposite direction and the indicator come to halt when the two are equal. This instrument is useful for resistance in range 100µΩ to 5Ω.
Now we can have two possible connections of ammeter and voltmeter, shown in the figure below.
Ammeter Voltmeter Method
Now in figure 1, the voltmeter measures voltage drop across ammeter and the unknown resistance, hence
Hence, the relative error will be,
For connection in figure 2, the ammeter measures the sum of current through voltmeter and resistance, hence
The relative error will be,
It can be observed that the relative error is zero for Ra = 0 in first case and Rv = ∞ in second case. Now the questions stand that which connection to be used in which case. To find out this we equate both the errors
Hence for resistances greater than that given by above equation we use the first method and for less than that we use second method.
Wheatstone Bridge
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
Combining the above two equations we get the famous equation –
Substitution Method
First the switch is place at position 1 and the ammeter is made to read a certain amount of current by varying r. The value of ammeter reading is noted. Now the switch is moved to position 2 and S is varied in order to achieve the same ammeter reading as it read in the initial case. The value of S for which ammeter reads same as in position 1, is the value of unknown resistance R, provided the EMF source has constant value throughout the experiment.
We normally utilize very small amount of current for such measurement, but still owing to high resistance chances of production of high voltages is not surprising. Due to this we encounter several other problems such as-
Hence to solve the problem of leakage currents or capacitive currents we use a guard circuit. The concept of guard circuit is to bypass the leakage current from the ammeter so as to measure the true resistive current. Figure below shows two connections on voltmeter and micro ammeter to measure R, one without guard circuit and one with guard circuit.
In the first circuit the micro ammeter measures both capacitive and the resistive current leading to error in value of R, while in the other circuit the micro ammeter reads only the resistive current.
Loss of Charge Method
However the above case assumes no leakage resistance of the capacitor. Hence to account for it we use the circuit shown in the figure below. R1 is the leakage resistance of C and R is the unknown resistance.
We follow the same procedure but first with switch S1 closed and next with switch S1 open. For the first case we get
For second case with switch open we get
Using R1 from above equation in equation for R’ we can find R.
G is the guard terminal. Now we can also represent the resistor as shown in the adjoining figure, where RAG and RBG are the leakage resistances. The circuit for measurement is shown in the figure below.
Megohm Bridge
It can be observed that we actually obtain the resistance which is parallel combination of R and RAG. Although this causes very insignificant error.
Megger is one of the most important measuring device used by electrical engineers and is essentially used for measuring insulation resistance only. It consists of a generator which can be hand driven or nowadays we have electronic megger.
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