A voltmeter with resistance RV is connected across the terminals of a battery of emf and internal resistance r. Find the potential difference Vmeter measured by the voltmeter.

voltage measured by the voltmeter = (E × RV)/(r + RV)

Explanation:

The circuit diagram for this description is presented in the attached image.

The internal resistance of an emf source is modelled to be in series with the source.

Therefore, the end product is a circuit with the battery in series connection with the internal resistance and resistance of the volunteer. The voltage picked up by the volunteer is the voltage across resistor RV.

Total resistance in the circuit = (r + RV) ohms (since both resistors are in parallel)

Current produced by the emf source = E/(Total resistance) = E/(r + RV)

The voltage across resistor RV = current flowing through this resistor × its resistance.

Since all the circuit elements are in series with each other, same current, E/(r + RV) flows through them all

Voltage across RV = voltage measured by the voltmeter = [E/(r + RV)] × RV = (E × RV)/(r + RV) = (E.RV)/(r + RV)