Unlike the idealized voltmeter, a real voltmeter has a resistance that is not infinitely large. part a a voltmeter with resistance rv is connected across the terminals of a battery of emf e and internal resistance r. find the potential difference vmeter measured by the voltmeter.

The EMF of the battery includes the force to to drive across its internal resistance. the total resistance:

R = internal resistance r + resistance connected rv

R = r + rv

Now find the current:

V 1 = IR

I = R / V1

find the voltage at the battery terminal (which is net of internal resistance) using

V 2 = IR

So the voltage at the terminal is:

V = V2 - V1

This is the potential difference vmeter measured by the voltmeter.