To demonstrate that a current measuring device has finite non-zero resistance.
It measures the potential difference across an electric component such as resistor or capacitor, Inductors etc. It is always connected in parallel with the electric component whose potential difference is to be measured. Voltmeter has very large resistance so that the current in the electric component does not change while measuring it. A voltmeter should not be connected in series, if you connect it in series then very insignificant current will pass through because of its high resistance and the circuit will behave as an open circuit.
It measures the current in the circuit. As it measures the current in the circuit, it is always connected in series with the electric component in which current needs to be measured. Because of the ammeter connected in series its resistance should be very low so that it does not affect the current flowing through that electric component also if an ammeter connected in parallel then very high current will pass through the ammeter as it has very low resistance which in turn will burn the fuse or damage the ammeter.
A basic law regarding flow of currents was discovered by G.S. Ohm in 1828, long before the physical mechanism responsible for flow of currents was discovered, by considering a conductor through which a current I is flowing and let V be the potential difference between the ends of the conductor.
Then Ohm’s law states that,
V µ I or, V = R I
R = V/ I
where the constant of proportionality R is called the resistance of the conductor. The SI unit of resistance is ohm. The resistance R not only depends on the material of the conductor but also on the dimensions of the conductor.