Ideal Voltmeters of DC Circuits

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I've read that an ideal voltmeter would have infinite resistance. I've done some searching and I've found that the infinite resistance ensures that no current is diverted through the voltmeter. Why is that? I thought it would be the other way around and essentially "eat up" the current ...
 
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I = V/R

If R->infinity then I -> 0.

You've got it inverted somehow.
 
A voltmeter is connected in parallel over a circuit. If the voltmeter has a very large resistance then very little current will flow through it and it will have a very small (disturbing) influence on the circuit. If it had a small resistance on the other hand current would "leak out" of the circuit into the voltmeter and thereby causing the circuit readings to change when it is connected - an undesirable effect, since we want to know what the citcuit is doing when it (the voltmeter) is not connected.
 

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