Voltmeter

                 It is a device to measure the potential difference between two points in a circuit. Voltmeter is connected across the two points in circuit across which the potential difference is to be measured i.e it is connected in parallel to the cicuit because voltage is same in parallel combination. A perfect volmeter of 100% accuracy must have infinite resistance so that no current flows through voltmeter without altering the voltage to be measured.

Galvanometer

                          It is a device used for detection and measurement of small currents. It is connected in series to the circuit through which the current is to be measured. It is very sensitive. It consist of arc like scale which is calibrated up to some digits.

Galvanometer as a Voltmeter

Galvanometer can be converted into voltmeter by connecting very high resistance in series with it.

Working

              When apply a high resistance in series with galvanometer, basically we make the current flow very small. Suppose we apply resistance to galvanometer and keep it constant, then 

                                                            I is proportional to V

As there is very high resistance to current, the minute current flows and we can say that it is equivalent voltage. Quite wrong to say. But, actually the deflection for current is equal to the deflection for voltage at that instant or configuration of system.

Desired Range Voltmeter

                                                Galvanometer can be converted to desired range voltmeter. Consider a galvanometer of resistance Rg, connected to a battery of voltage V and variable resistor of resistance R in series with galvanometer as shown

Changing the resistor R the maximum deflection of the galvanometer is attained. It means that galvanometer can now measure up to voltage V.

The total voltage V is equal to       V = Ig(Rg + R)

                                                          V/Ig = Rg + R

                                                           R = (V/Ig) - Rg

Where Rg is the resistance of the galvanometer. Knowing all the values and putting the desired voltage value for desired range voltmeter in above equation, resistance R is calculated. Resistor of that much resistance is connected in series with galvanometer to make it desired range voltmeter.