# Archived How to include resistance of wire and voltmeter in Kirchhoff equations

#### jey1234

1. Homework Statement
I'm doing a lab report and the last question is, how would your measurements (currents and voltages across each resistor) be affected if the resistance of the wires is 0.01 Ω and the internal resistance of the voltmeter is 10 MΩ?

2. Homework Equations
3. The Attempt at a Solution
I'm going to take a guess here. For the wire, do I just pretend there is a resistor of 0.01 Ω right next to one of the power supplies? Or do I have to add it in each of the three branches? For the voltmeter, do I add a 10 MΩ resistor in parallel to each of the three resistors, find their equivalent resistance and then use that for the Kirchhoff current equations? Thanks.

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#### CWatters

Homework Helper
Gold Member
In short you would need to replace all wires with 0.01Ohm resistors and place a 10MOhm resistor between the leads of your otherwise ideal voltmeter.

So in this circuit the end result is to put 0.01 Ohm resistors in series with all of the resistors. Putting a 0.01 Ohm in series with a 50, 100 or 200 Ohm resistor will have virtually no effect because 50 >> 0.01.

When you use the modified voltmeter to measure the voltage across any of the resistors the 10MOhm resistor will be in parallel with the resistor. This will have no significant effect because 10MOhm >> 50, 100 or 200 Ohm.

So in this circuit there will be no significant change to the measured voltages an currents. In other circuits with different component values there could be a significant change.

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"How to include resistance of wire and voltmeter in Kirchhoff equations"

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