Voltmeter Readings: Changes with Contact Resistance Increase

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When the contact surface between two conductors is increased, (battery and wire) what happens to the voltmeter reading?

If cross-sectional area of wire is increased, current increases but what happens to potential difference on the circuit? Contact resistance is what's varying surely... or does contact resistance stay constant and pd changes?
 
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a larger, contact surface as well as larger wire gauge will allow more current flow. However a battery outputs a maximum current. A poor connection is a resistance point, however once resistance is effectively zero then a larger surface area will only support a higher current providing the power supply can deliver such and the circuit load requires the current
 
Contact resistance between two surfaces is a complicated business. If there is sufficient pressure to ensure a large actual area of contact and if the surfaces start off very clean, then the effect of the small length of metal ( much less than a millimetre) with a smaller cross sectional area than with wire will not be much. But if the surfaces are not perfectly clean then there can be a microscopic non-conducting layer between the metals. Wiki has a lot to say about this.

If you want to eliminate the effects of contact resistance when trying to measure resistance, it is normal to make your PD measurement inside, rather than outside, the connections to your source of current so you are measuring the actual drop across the component, not including crocodile clips or whatever. You can assume that the current taken by your voltmeter is low enough not to affect the PD dropped by the contact resistance of the voltmeter probes.

But you will always have the problem of deciding what is the actual length of the wire you are measuring if you are trying to measure resistivity.