Voltmeter connected across an open switch

[PFuser1232]

I have once read that if a voltmeter is connected across an open switch in a circuit, the emf of the source is shown on the voltmeter, because this connection completes the loop, making a tiny current flow through the circuit, and since the voltmeter has a huge resistance, the entire voltage drop is due to the voltmeter. But won't connecting a voltmeter across a switch also form a series circuit? And, according to my knowledge, voltmeters show no reading when connected in series.

 

[Dadface]

The voltmeter will form a series circuit and the resistance of the voltmeter itself can be considered as one of the series resistors. If the values of all the resistances in the circuit are known the voltage across the voltmeter resistance (the measured voltage) can be calculated using Ohm's law. If the rest of the circuit has a total resistance which is negligible compared to the resistance of the voltmeter the voltmeter will measure the emf of the source.

 

[PFuser1232]

The voltmeter will form a series circuit and the resistance of the voltmeter itself can be considered as one of the series resistors. If the values of all the resistances in the circuit are known the voltage across the voltmeter resistance (the measured voltage) can be calculated using Ohm's law. If the rest of the circuit has a total resistance which is negligible compared to the resistance of the voltmeter the voltmeter will measure the emf of the source.

I understand. But if that's the case (if measuring voltage was that simple) why must the voltmeter always be connected parallel to a component? Why can't we just connect it in series with the source to measure the emf of the source? According to my knowledge, voltmeters connected in series give no reading at all.

 

[Dadface]

The voltage across anyone component in a series circuit is equal to the current times the resistance of that component.The bigger the resistance the bigger the voltage. If you wanted to measure the voltage across anyone component you would connect your voltmeter in parallel with that component. An ideal voltmeter would have an infinite resistance and when connected in parallel, the effective resistance of the parallel combination would equal the resistance of the component.*

If you connected the voltmeter in series you would not be measuring the voltage across anyone component but would be measuring the voltage developed across the resistance of the voltmeter. If the rest of the circuit resistance is "very low" the measured voltage would be very close to the emf of the source.

* A real voltmeter with large but finite resistance would introduce an error due to the effective parallel resistance becoming smaller when the voltmeter is connected. The bigger the difference between component resistance and voltmeter resistance the smaller the error.

You can work it all out using Ohm's law and the resistors in parallel equation.

 

[PFuser1232]

The voltage across anyone component in a series circuit is equal to the current times the resistance of that component.The bigger the resistance the bigger the voltage. If you wanted to measure the voltage across anyone component you would connect your voltmeter in parallel with that component. An ideal voltmeter would have an infinite resistance and when connected in parallel, the effective resistance of the parallel combination would equal the resistance of the component.*

If you connected the voltmeter in series you would not be measuring the voltage across anyone component but would be measuring the voltage developed across the resistance of the voltmeter. If the rest of the circuit resistance is "very low" the measured voltage would be very close to the emf of the source.

* A real voltmeter with large but finite resistance would introduce an error due to the effective parallel resistance becoming smaller when the voltmeter is connected. The bigger the difference between component resistance and voltmeter resistance the smaller the error.

You can work it all out using Ohm's law and the resistors in parallel equation.

So connecting an ideal voltmeter in series would always measure the supply voltage?

 

[Dadface]

Yes it would.

 

[Drakkith]

So connecting an ideal voltmeter in series would always measure the supply voltage?

Since an ideal voltmeter would have infinite resistance, yes. The voltmeter would act as an open in the circuit and the voltage drop for that entire leg of the circuit (which may be equal to the supply voltage) would be measured across it.

 

[Karan T]

I think that when a voltmeter is connected in series, it will act as a normal galvanometer connected in a circuit containing a high resistance.

 

[olaney]

Galvanometer? That is a totally obsolete instrument!
Suffice to say, if two identical voltmeters are connected in series across 100V, each will individually read 50V.