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Let R be resistance of the resistor near the voltmeter, and I' be the current flow through it. Thus, the voltage between two nodes of the resistor is


The voltage is the same with reading of the voltmeter. Hence,



Then the voltmeter is substituted with an ammeter. We need to find the relation between reading of the ammeter and other variables. If an ammeter is connected to a resistor, no current will flow through the resistor.
Now, consider only circuit like shown below.
Using simple ohm's law, we can get

where Rtot is total resistance of the circuit.

We want the current flow through the resistor has the same magnitude with I', so that it becomes zero if we do superposition with these two conditions (initial condition and condition like picture above).

The current flow through the ammeter is the same with I0',


By using these equations, we can get



Substitute I'R, and we get

It's equal with reading of the ohmmeter, because it reads the total resistance of the circuit.


That's my solution.
If you have any question, correction, or comment, please leave a comment below.
Thank you.

Solution - Complex CircuitSocialTwist Tell-a-Friend

2 comments

sanchar said... @ June 18, 2010 at 7:38 PM
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sanchar said... @ June 18, 2010 at 7:40 PM

well, that was an admirable solution but you probably made a simple thing look a bit complicated. just consider a battery of emf E, the resistance around the voltmeter as R and all the other resistance between battery and resistance R as R1. writing two equations for voltmeter and ammeter directly gives the above result. no brains!!!

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