Input resistance (Input impedance)

[wavingerwin]

Homework Statement

A digital voltmeter is used to measure the resistance and voltage of a circuit.
The resistance and voltage measured is used to calculate current flowing.

What errors does the input resistance of the voltmeter introduce into the determination of current?

Homework Equations

I don't know whether this is useful or not but:

$$Input resistance = Z = R_{Test}\frac{V_{2}}{\left(V_{1}-V_{2}\right)}$$

The Attempt at a Solution

Well, my idea is that it won't introduce any error since both voltage and resistance are measured with the input resistance of the voltmeter in place.

When the values are used to calculate current, the 'errors' associated with voltage and resistance would cancel out. I cannot proof it mathematically though.

Thanks in advance for any suggestion!

 

[anathema]

Hello,

Thank you for your post. I would like to offer some insights on the potential errors that the input resistance of the voltmeter can introduce into the determination of current.

First, let's define what input resistance is. Input resistance is the resistance that the voltmeter itself adds to the circuit when it is connected to measure voltage. This resistance is usually very high, in the range of megaohms, and can be considered negligible compared to the resistance in the circuit being measured. However, it is still important to take into account when calculating current.

One potential error that the input resistance can introduce is a voltage drop. Because the input resistance is not zero, it will create a small voltage drop in the circuit being measured. This voltage drop will be added to the actual voltage measured by the voltmeter, resulting in a slightly higher voltage reading. This, in turn, will lead to a higher calculated current value.

Another potential error is related to precision and accuracy. The input resistance of the voltmeter can affect the precision and accuracy of the voltage measurement. The higher the input resistance, the more sensitive the voltmeter is to small changes in the circuit. This can result in a higher degree of uncertainty in the voltage measurement, which can lead to errors in the calculated current value.

Lastly, the input resistance can also affect the stability of the circuit being measured. When a voltmeter is connected to a circuit, it can act as a load and change the behavior of the circuit. This can result in fluctuations in the voltage and resistance values, which can lead to errors in the calculated current.

In conclusion, while the input resistance of the voltmeter may seem insignificant, it can introduce errors in the determination of current. These errors can be minimized by using a voltmeter with a lower input resistance, ensuring proper calibration, and taking into account the potential effects on the circuit being measured.

I hope this helps to answer your question. Best of luck with your research!