Page 322 - Electrician - TT (Volume 1)

ELECTRICIAN - CITS

Fig 1

In both the cases, if readings of the ammeter and voltmeter are taken, then the measured value of resistance is
given by
Voltmeter reading V
R Ammeter reading = I
m

The measured value of resistance Rm, would be equal to the true value R, provided the ammeter resistance is
zero and the voltmeter resistance is infinite, to make the circuit condition undisturbed.
However, in practice this is not possible, and hence, both the methods give inaccurate results. But the error in
measurement could be reduced under different values of resistance to be measured as explained below.
Circuit (Fig 1a): In this circuit, the ammeter measures the true value of the current through the resistor. But the
voltmeter does not read the true voltage across the resistance. On the other hand, the voltmeter measures the
voltage drop across the resistance and also the ammeter.
Let R be the resistance of the ammeter.
a
Then the voltage drop across the ammeter V = IR a
a
V V + V I R + R
I
R = = R a = a
mt
I I I
R R
= R + R ............Eqn.(1)
a
true value of resistance R = R R ... Eqn.(2)
a
m1
From equation 2, it is clear that the measured value of resistance is higher than the true value. It is also clear from
the above equation, that the true value is equal to the measured value only if the ammeter resistance R is zero.
a

Conclusion: From equation 3, it is clear that the error in measurement would be small if the value of resistance
under measurement is large as compared to the internal resistance of the ammeter. Therefore, the circuit shown
in Fig 1(a) is most suitable for measuring high resistance values only.

Circuit (Fig 1b): In this circuit the voltmeter measures the true value of the voltage across the resistance but the
ammeter measures the sum of currents through the resistance and the voltmeter.
Let R be the resistance of the voltmeter. Then the current through the voltmeter
V
V
I =
V R
V
Measured value of the resistance

309

CITS : Power - Electrician & Wireman - Lesson 50-53 CITS : Power - Electrician & Wireman - Lesson 50-53