Limitation of Resistance Measurement using Voltmeter-Ammeter Method


The voltmeter-ammeter method is a widely used method for measuring the resistance of a circuit. In this method, a voltmeter is connected in parallel with the resistance to measure the voltage drop across it, and an ammeter is connected in series with the resistance to measure the current passing through it. However, the accuracy of the measurement is limited by the accuracy of the instruments used. In this article, we will discuss the limitation of resistance measurement using the voltmeter-ammeter method.


The accuracy of the measurement depends on the accuracy of the instruments used. In this case, the voltmeter and ammeter are guaranteed for accuracy within 2% of full scale. This means that the actual reading of the instrument can be off by 2% of the full scale reading.


The limitation of resistance measurement can be calculated using the following formula:

ΔR/R = (ΔV/V + ΔI/I)

Where,
ΔR/R = the fractional error in resistance
ΔV/V = the fractional error in voltage measurement
ΔI/I = the fractional error in current measurement

Substituting the given values, we get:

ΔR/R = (0.02 + 0.02) = 0.04

Therefore, the fractional error in resistance measurement is 0.04 or 4%. This means that the resistance measurement can be off by as much as 4% of the actual value.


To determine the limit of resistance measurement, we can rearrange the formula as follows:

ΔR = R × (ΔV/V + ΔI/I)

Substituting the given values, we get:

ΔR = 100 Ω × (0.02 + 0.02) = 4 Ω

Therefore, the limit of resistance measurement is 4 Ω. This means that the resistance can be measured accurately only if it is greater than 4 Ω. If the resistance is less than 4 Ω, the measurement will be inaccurate due to the limitations of the instruments used.


In conclusion, the voltmeter-ammeter method is a simple and widely used method for measuring the resistance of a circuit. However, the accuracy of the measurement is limited by the accuracy of the instruments used. In this case, the limit of resistance measurement is 4 Ω, which means that the resistance can be measured accurately only if it is greater than 4 Ω.