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Question asked.

So this question came up as was revising past paper questions for the IB Physics exam.

While I understand that the resistance in an ideal ammeter is supposed to be zero as you're trying to measure the current without anything affecting it such as resistance, I was wondering why the resistance of an ideal voltmeter is better being infinite.

The answer to the question was B, by the way.

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To measure the potential difference accross a component with a voltmeter, you need to connect the voltmeter in parallel with the component. Then the current can either flow accross the component (say a resistor) or accross the voltmeter. Since current is conserved ($I_{in} = I_{out}$) at a junction, the total current in will be the sum of the current that passes through the resistor and through the voltmeter.

By Ohm's law, current will take the path of least resistance, so if the resistances were around the same then about half of the current would flow through the voltmeter and half through the circuit element. To avoid this, we make the resistance of the voltmeter as high as possible (infinite would be idea) so that very little current flows through it and the circuit behaves almost as it would if the voltmeter were not connected.

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  • $\begingroup$ If current does theoretically not pass through it due to the current taking the path of least resistance, then how are we able to measure the potential difference? I understand that we see how the current differs before and after it enters a component such as a lamp, for example, but how are we able to measure the difference in voltage if it does not pass through the voltmeter? $\endgroup$ – Rogue Apr 22 '18 at 14:37
  • $\begingroup$ Well the idea is the higher the resistance is the better it is but the more sensitive you need to be able to measure the small current. There will always be a small amount of current that flows. Since the voltage is the same across two parallel circuit elements, if we can measure the voltage across the resistor in the voltmeter, we also know the voltage across the circuit element. These instruments are sensitive enough that only a very small current is needed so we make the resistance very high. $\endgroup$ – fhorrobin Apr 22 '18 at 14:43
  • $\begingroup$ Ahh, I see. Thanks for the information. It's interesting to see how circuits truly do work. $\endgroup$ – Rogue Apr 22 '18 at 14:48
  • $\begingroup$ Glad I could help. It would be great if you could choose this as accepted answer if you found it helpful. $\endgroup$ – fhorrobin Apr 22 '18 at 14:50
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    $\begingroup$ @Rogue As an illustration of a voltmeter drawing very, very little current remember that a gold leaf electroscope can be used as a voltmeter although the scale will be non-linear. The resistance of the gold leaf electroscope is a function of the insulator which separates the case from the leaf and the air surrounding them. $\endgroup$ – Farcher Apr 22 '18 at 15:56

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