# Ammeter & Voltmeter

## What is an Ammeter?

An ammeter is an instrument used to measure the electric current in an electric circuit.

• An ammeter is a modified form of a galvanometer.
• An Ammeter works on the principle that, when a current carrying loop is placed in a magnetic field, it will experience a magnetic force which produces a torque in the loop.
• Most of the other electrical instruments like Galvanometer, Voltmeter etc. work on this principle.

### Use of Galvanometer as an Ammeter

If a galvanometer is used as an ammeter to measure amount of electric current flowing in a circuit, then two incidence may happen –

1. If the galvanometer has large resistance, it will effect and change the actual value of electric current in circuit and actual current reading will not be obtained.
2. A large amount of current in the circuit may damage or burn the galvanometer coil.

Thus, a galvanometer can not be used directly as an ammeter to measure a current in circuit.

• For measuring a current in a circuit, we will require a device of very low or practically zero resistance.
• Thus, a galvanometer is modified and converted into an ammeter which satisfy all of the above conditions.
• In conversion of a galvanometer into an ammeter, a low value resistance is added in the device and connected in parallel to the coil. This process is called shunting of coil.

## Shunt

A Galvanometer is converted into an Ammeter by connecting a low resistance parallel to the galvanometer coil as shown in figure. This resistance is called a shunt.

### Conversion of Galvanometer into Ammeter

In conversion of a galvanometer into an ammeter, a shunt is added in the device and connected in parallel to the coil.

Consider that –

• ( G ) is the coil resistance and ( S ) is shunt resistance of a galvanometer.
• ( I ) is the total current in the circuit which has to measure.
• ( I_g ) is the current flowing through the galvanometer coil corresponding to which galvanometer gives the full scale deflection.

Therefore, remaining current flowing through the shunt will be \left ( I - I_g \right )

Since, ( G ) and ( S ) are connected in parallel so the voltage across them is same.

Therefore, \quad I_g G = \left ( I - I_g \right ) S

Or, \quad S = \left ( \frac {I_g}{I - I_g} \right ) G ……. (1)

• This is the required value of shunt resistance to be added in parallel to the coil of meter.
• The converted device can be used safely as ammeter of range ( 0 ) to ( I ) ampere.

### Effective Resistance of Ammeter

Total effective resistance ( R_{e} ) of ammeter becomes –

\left ( \frac {1}{R_{e}} \right ) = \left ( \frac {1}{G} \right ) + \left ( \frac {1}{S} \right ) = \left ( \frac {G + S}{GS} \right )

Or, \quad ( R_{e} ) = \left ( \frac {GS}{G + S} \right ) ……. (2)

Since ( G >> S ) , so \left ( G + S \right ) \simeq G

Hence, \quad ( R_{e} ) = \left ( \frac {GS}{G} \right ) = S

• Thus an ammeter is a low resistance device.
• Resistance of an ideal ammeter is zero.
• An ammeter is always connected in series of in the circuit of which current has to measure.

### Increasing the Range of Ammeter

Consider that an ammeter is capable of measuring a maximum current ( I_1 ) . We have to modify it so that it become capable of measuring a current up to ( I_2 ) .

Let, \quad \left ( \frac {I_2}{I_1} \right ) = n

Now, from equation (1) for an ammeter, we have –

S = \left ( \frac {I_g}{I - I_g} \right ) G ……. (1)

Since, maximum allowable current through the ammeter coil is ( I_1 ) , we can replace ( I_g ) \ \text {and} \ ( I ) in equation (1) by ( I_1 ) \ \text {and} \ ( I_2 ) respectively.

Therefore, \quad S = \left ( \frac {I_1}{I_2 - I_1} \right ) G

Or, \quad S = \left [ \frac {G}{\left ( \frac {I_2}{I_1} - 1 \right )} \right ] = \left ( \frac {G}{n - 1} \right ) ………. (3)

Hence, amount of shunt resistance \left [ S = \left ( \frac {G}{n - 1} \right ) \right ] that should be added in parallel to the coil of ammeter to increase its capacity.

## Voltmeter

A voltmeter is an instrument used to measure the potential difference across the two ends of a circuit element.

### Use of Galvanometer as a Voltmeter

• If we connect a simple galvanometer in parallel to a circuit to measure voltage, it will draw some current from circuit and hence potential difference between the points as recorded by the galvanometer will not be accurate.
• For accurate measurement of the potential difference, it is essential that the current between the two points of measurement should remain the same after connecting the measuring device.
• This is only possible if the resistance of the measuring device is very high or infinite, so that it may not draw any current.
• Hence, to measure potential difference, a galvanometer is modified and converted into a device whose resistance is very large.

### Conversion of Galvanometer into Voltmeter

A galvanometer can be converted into a voltmeter by connecting a large resistance in series to the galvanometer.

Consider that –

• ( R ) is the resistance connected in series to a galvanometer of coil resistance ( G )
• ( V ) volt is the potential difference to be measured by the voltmeter.
• ( I_g ) is the current flowing in the circuit corresponding to which the voltmeter gives the full scale deflection.

Now, potential difference between points A and B is given by –

V = I_g R + I_g G

Or, \quad V = I_g \left ( R + G \right )

Therefore, \quad ( R + G ) = \left ( \frac {V}{I_g} \right )

Or, \quad R = \left ( \frac {V}{I_g} \right ) - G ……… (1)

Hence, amount of resistance \left [ R = \left ( \frac {V}{I_g} \right ) - G \right ] should be added in series to the coil of Galvanometer to work as a Voltmeter.

### Effective Resistance of Voltmeter

Effective value of resistance of a voltmeter is given by –

( R_{e} ) = ( R + G ) which is very high.

• Thus, voltmeter is a high resistance device.
• Resistance of an ideal voltmeter is infinite.
• A voltmeter is always connected in parallel to the element across which voltage has to measure.