# Ammeter , Voltmeter

### Ammeter :

An Ammeter is an instrument used for measuring current in electrical circuits. A galvanometer when used to measure current is called an ammeter. A galvanometer is a low resistance instrument.
A large current passing through it may damage the instrument. To measure the current in a branch of the circuit it is always connected in series with the branch.

Due to the low resistance of the meter, the resistance of the circuit does not increase for all practical purposes on its introduction in the circuit and therefore the current in the circuit also remains unaffected.

### Changing the range of an ammeter :

Suppose the ammeter gives full scale deflection when a current Ig flows through it.

Now if we want to convert the reading of the ammeter in such a manner that it gives full scale deflection for a higher current I in the branch of the circuit, we connect a small resistance S in parallel to the coil of the galvonometer coil of the meter, which has a reisistance G.

The resistance value is so chosen that out of the total current I only Ig flows through the coil and the remaining current flows through S

As potential difference across S = potential difference across G.

=> (I – Ig)S = Ig G

=> S = Ig G/(I – Ig)

### Voltmeter :

A voltmeter is an instrument used for measuring potential difference across the two ends of a current carrying conductor. It is connected in parallel with the conductor across which the potential difference is to be measured.

The current through the conductor should not change on connecting the voltmeter, and so the voltmeter should draw a very small current, i.e. its resistance has to be high.

When a galvanometer is used to measure potential difference across the ends of a current carrying conductor, a high resistance R is connected in series with the galvanometer.

Consider the diagram shown below. Suppose the galvanometer gives full scale deflection when a current Ig passes through its coil. If G is resistance of the galvanometer coil then :

Potential difference to be measured = Ig(G + R)

=> R = ( V/Ig) − G

So, effectively the voltmeter has resistance = Rv = (G + R)

In practice Rv is very large compared to G. An ideal voltmeter should possess infinite resistance.

Example : A galvanometer has a resistance of 30 ohm and a current of 2mA is needed to give a full scale deflection. What is the resistance needed and how is it be connected to convert the galvanometer

(a) into an ammeter with a range of 0.3 ampere.

(b) into a voltmeter with a range of 0.2 volt.

Solution : Here galvanometer resistance G = 30Ω and full scale deflection current Ig = 2 mA

(a) To convert the galvanometer into an ammeter of range 0.3 ampere, a resistance of value ‘ S ‘ is connected in parallel with it such that the current through G should not be more than Ig= 0.3A and I − I should pass through S.

(I − Ig) S = Ig G

S = Ig G/(I−Ig)

= 2 x 10−3 x 30/(0.3−2 x 10−3)

= 0.2 Ω

(b) To convert the galvanometer into a voltmeter of range 0.2 volt, a resistance R is connected in series with it such that

V = Ig (R + G)

i.e. 0.2 = 2 x 10-3 (30 + R)

R = 100 – 30 = 70 ohms

R = 70 ohm.

Hence to convert the galvanometer into an ammeter of the desired range a shunt resistance ( a small valued resistance ) of 0.2Ω is connected parallel to the meter.

This shunt resistance gives us a low resistance instrument with a deflection current Ia = 0.3 ampere, while the current through the galvanometer is 2 mA.

To convert the galvanometer into a voltmeter of the desired range, a high resistance (Rs) is connected in series with the galvanometer.

The equivalent meter resistance is Req = 30 + 70 = 100 ohm. In this case most of the voltage appears across the series resistor. The current through the voltmeter is 2 mA.

Exercise : A voltmeter has a resistance of G ohm and range of V volt. Calculate the resistance to be used in series with it to extend its range to λV volt , where λ is a positive number.