Understanding DC Voltmeter Sensitivity and Calculating Current: A Detailed Guide

When dealing with electrical measurements, particularly with DC voltmeters, it's crucial to understand the underlying principles of sensitivity, resistance, and current. This guide will help you comprehend how to calculate the current through a voltmeter when measuring half full scale in the 100 V range, given its sensitivity.

Introduction to DC Voltmeters and Sensitivity

A DC voltmeter measures the voltage across a circuit. Its sensitivity, defined as 1000 ohms per watt, indicates the resistance it introduces into the circuit for every watt of power utilized. Understanding this concept and how it impacts the current flow is essential.

Step-by-Step Calculation

A) Determining the Half Full Scale Voltage

First, it's important to establish the half full scale voltage. Since the full scale voltage of the 100 V range is 100 V, the half full scale would be:

V frac{100,text{V}}{2} 50,text{V}

B) Understanding the Sensitivity

The sensitivity of the voltmeter is specified as 1000 ohms per watt. This means that for every watt of power, the voltmeter has an equivalent resistance of 1000 ohms.

C) Calculating the Voltmeter Resistance

The power ( P ) consumed by the voltmeter can be calculated using the formula:

P V times I

Rearranging this equation, we find:

I frac{P}{V}

The resistance ( R ) of the voltmeter can then be determined using the sensitivity equation:

R 1000,text{ohms/watt} times P

Since ( P frac{V^2}{R} ), we can substitute and rearrange to find:

R frac{V^2}{P}

This leads to:

I frac{V}{R} frac{V}{1000,text{ohms/watt} times frac{V}{I}}

Upon simplification:

R 1000 times I implies I frac{50,text{V}}{1000 ,text{ohms}} 0.05,text{A} 50,text{mA}

Therefore, when the voltmeter measures half full scale in the 100 V range, the current through the voltmeter is 50 mA.

Conclusion

In summary, to accurately measure the current through a DC voltmeter in its 100 V range under half full scale conditions, the sensitivity provided is crucial. Correctly calculating the resistance and applying Ohm's law allows us to determine the current precisely.

Additional Insights

Many responses suggest that the sensitivity is more appropriately expressed as ohms per volt (ohm/volt) or ohm-volt. Indeed, if we adopt this approach, the resistance of the meter on the 100 V range would be:

R 100,text{V} times 1000,text{ohms/V} 100,000,text{ohms} 100,text{kohms}

With 50 V applied, the current can be calculated using Ohm's law:

I frac{50,text{V}}{100,000,text{ohms}} 0.5,text{mA}

This approach provides a clear and accurate method for evaluating the meter's performance and current flow.

Conclusion

This guide provides a detailed and accurate method for calculating the current through a DC voltmeter when it measures half full scale in the 100 V range, based on its specified sensitivity. Understanding and applying these principles correctly is essential for electrical measurements and troubleshooting.