Resistance is classified
into three categories for the sake of Measurement. Different categories of
Resistance are measured by different technique. That’s why they are classified.
They are classified as

**Low Resistance:**Resistance having value 1Ω or below are kept under this category.

**Medium Resistance:**This category includes Resistance from 1Ω to 0.1 MΩ.

**High Resistance:**Resistance of the order of 0.1 MΩ and above is classified as High resistance.
In this section, we will
discuss the method of measurement of Medium Resistance. The different methods
used for Medium resistance are as follows:

·
Ammeter
Voltmeter method

·
Substitution
Method

·
Wheatstone
Bridge Method

·
Ohmmeter
Method

###
**Ammeter Voltmeter
Method:**

There are two possible connections for the
measurement of Medium Resistance using Ammeter Voltmeter Method as shown in
figure below:

In both the cases,
the reading of Voltmeter and Ammeter is taken. If the Voltmeter reading is V
and Ammeter reading is I then the measured Resistance will be

This measured
Resistance Rm will be the true value of the Resistance if and only if the
Resistance of Ammeter is zero and that of Voltmeter is infinite. But actually
this is not possible to achieve zero resistance Ammeter and infinite Resistance
Voltmeter. Therefore measured value of resistance Rm will deviate from the true
value R (Say).

So we will discuss
both the circuit individually and will calculate the percentage error in the
measurement.

**Case1:**

We consider first kind of connection as
shown in figure 1 above. It is clear from the figure that Voltmeter is
measuring the Voltage drop across the Ammeter as well as resistor. So V = Va +
Vr

Let current measured
by Ammeter = I

Therefore, measured Resistance
Rm = V/I

So, Rm = (Va+Vr) / I
=(IRa+IR) / I = Ra+R

Therefore, the
measured Resistance is the sum of Resistance of Ammeter and true Resistance.
Therefore measured value will only represent true value if Ammeter Resistance
Ra is Zero.

True value of
Resistance R = Rm –Ra

= Rm(1-Ra/Rm)

Relative Error = (Rm-R)/R
= Ra/R

**Therefore, Relative Error will be less if the true value of Resistance to be measured is high as compared to the internal Resistance of Ammeter. That’s why this method should be adopted when measuring high Resistance but it should be under Medium Resistance category.**

**Case2:**

We will consider second connection in which
Voltmeter is connected in which Voltmeter is connected toward Resistance R
whose value is to be measured.

It is obvious from
figure that Ammeter will read the current flowing through the Voltmeter and
Resistance R. Therefore current measured by Ammeter Ia = Iv+Ir

So, Ia = Iv+Ir

= V/Rv+V/R where Rv is Resistance of
Voltmeter and V is Voltmeter reading.

Measured Resistance
Rm = V/Ia

=
V/(V/Rv+V/R)

= RvR/(R+Rv)

=
R/(1+R/Rv) ….Dividing Numerator and Denominator by Rv

Therefore, true value
of Resistance R = RmRv/(Rv-Rm)

= Rm(1-Rm/Rv)

Therefore, true value of Resistance will only
be equal to measured value if the value of Voltmeter Resistance Rv is infinite.

If we assume that the
value of Voltmeter Resistance Rv is large as compared to the Resistance to be
measured R, then Rv>>>Rm

So, True value R =
Rm(1+Rm/Rv)

Thus from the above
equation it is clear that the measured value of Resistance is smaller than the true
value.

Relative Error = (Rm-R)/R

= -R/Rv

Therefore, it is
clear from the expression of Relative Error that, error in measurement will be
low if the value of Resistance under measurement is very less as compared to
the internal Resistance of Voltmeter.

This is the reason;
this method is used for the

**Contact Resistance Measurement**. As the value of**Contact Resistance is of the order of 20 micro Ohm**which is very less as compared to the internal Resistance of Voltmeter.
The Voltmeter Ammeter
Method for Cases1 and Case2 are simple method but it is not accurate method.
The error in the value of Resistance depends on the accuracy of Ammeter as well
as Voltmeter. If the accuracy of both the instrument are supposed 0.5% then
when both the instrument read near full scale, the error in measurement of Resistance
may vary from 0 to 1% while if both the instrument read near half scale then
error may double and so on.

However this method
is very useful where high accuracy is not required. The suitability of Case1 or
Case2 depends on the value of Resistance to be measured. The division point
between the two methods is at the Resistance for which both the method give
same Relative Error.

So, Ra/R = R/Rv

**For the Resistance greater than the value given above,Case1 is used while for the value of Resistance lower than R given above Case2 is used.**

**Check this Book for Electrical Measurement and Instrumentation. It is really awesome and concepts are dealt with very nicely.**

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