Voltmeter : A voltmeter is an instrument used to measure the potential difference across the two ends of a circuit element.
Conversion of galvanometer into voltmeter :
A galvanometer can be converted into a voltmeter by connecting a large resistance in series to the galvanometer.
Let G and R be the resistance of a Galvanometer and a conductor connected in series with it respectively.
Let V volt be the potential difference to be measured by the voltmeter.Let $I_{g}$ be the current flowing in the circuit .
Now potential difference between points A and B is given by :
$$V = I_{g}R + I_{g}G$$
$$V = I_{g}(R+G)$$
$$\therefore \ R + G = \frac{V}{I_{g}}$$
$$R = \frac{V}{I_{g}}-G$$
Effective Resistance of the voltmeter :
Effective value of resistance of the galvanometer is given by :
$$R^{'} = (R+G)$$
Which is very High
Thus , voltmeter is a high resistance device , Resistance of an ideal voltmeter is infinite.
Note : a voltmeter is always connected in parallel to the circuit component across which voltage is to be measured.