A voltmeter is essentially an ammeter, shown below

connected in series with a high resistance designed to limit the current through the resistor and meter.

The deflection of the meter is proportional to the current passing through, and the meter can be calibrated to read the whole voltage across the meter plus the series resistor. The resistor is chosen so that the voltmeter reads voltages within a certain range. Ideally a voltmeter should have infinite resistance so it does not alter any of the currents in the circuit, but real voltmeters always have infinite resistance.

Suppose the meter has resistanceand can pass a currentthen the total voltage across meter plus resistor is

Ifandthen to read voltages up to 10V we would have to solve

In principle voltages up to any magnitude can be measured this way.

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