# DC Ammeter : Construction, Working and Temperature Compensation

## What is DC Ammeter?

A DC ammeter is the instrument used for measuring the direct current (DC) flowing through an electrical circuit and is connected in series to the circuit under consideration.

## Construction of DC Ammeter

The construction of DC ammeter is similar to a galvanometer. The instrument has an internal resistance which should be much smaller in comparison to the resistance of the circuit. The basic movement of a DC ammeter is constituted by a PMMC d’Arsonval galvanometer. Thus, the basic construction of the DC ammeter remains the same as galvanometer.

The deflection of the pointer is in proportion to the current flowing in the moving coil.

Here, the maximum deflection of the pointer is produced by a very small current as the coil winding is very light and thin.

The large currents may destroy the coil winding. Therefore, to measure such large currents, the ammeter is provided with a resistor of very low resistance (generally less than 1 Ohm) and referred to as shunt connected in parallel to the instrument coil or meter movement. The **shunt **may be external or internal to the instrument.

The **external shunt** is made up of manganin or constantan with the low resistance. Whereas the **internal shunt** used with the basic movement is in the form of a constant temperature resistance wire encased within the instrument. However, more often external shunts are used to measure large currents.

When a large amount of current is to be measured, the major part of it must be bypassed via the shunt so that the dc ammeter does not get damaged.

## DC Ammeter Calculations

The basic configuration of an ammeter circuit is shown below.

Here, **R _{sh}** represents shunt resistance and

**R**is meter resistance (also known as coil circuit resistance or internal resistance of the movement)

_{m}From the figure above, we can say that the total current **I** is bifurcated into the meter current **I _{m}** (also termed as full scale deflection current of the movement

**I**) and shunt current

_{FSD}**I**, such that, on summing the total current I is I = I

_{sh}_{m}+ I

_{sh}

Total Current, **I = I _{m} + I_{sh}**

It necessitates that the voltage drop across the movement and the shunt must be the same. Thus, the required shunt resistance **R _{sh}** can be calculated.

Since, [latex] V_{s h}=V_{m} [/latex]

[latex] I_{s h} R_{s h}=I_{m} R_{m} [/latex]

⇒ [latex] R_{s h}=\frac{I_{m} R_{m}}{I_{s h}} [/latex] (Eqn 1)

Here, we know that: [latex] I_{s h}=I-I_{m}[/latex]

Substituting the value of **I _{sh}** from into Eqn (1), we get:

[latex]R_{s h}=\frac{I_{m} R_{m}}{I-I_{m}}[/latex]

Given the values of total current I, meter current I_{m} , and meter resistance R_{m} , the value of shunt resistance R_{sh} can be calculated using the relation the equation. Further, the above relation can be modified as:

[latex]\frac{R_{s h}}{R_{m}}=\frac{I_{m}}{I-I_{m}} & \text { or } \quad \frac{R_{m}}{R_{s h}}=\frac{I-I_{m}}{I_{m}} [/latex]

[latex]\frac{R_{m}}{R_{s h}}=\frac{I}{I_{m}}-1 & \text { or } \quad \frac{I}{I_{m}}=\frac{R_{m}}{R_{s h}}+1[/latex]

Here, term I/I_{m} represents the multiplying power of the shunt and is denoted by m.

Thus, equation can be written as:

[latex]m=\frac{R_{m}}{R_{s h}}+1 [/latex]

**[latex]R_{s h}=\frac{R_{m}}{m-1}[/latex]**

This equation is used to determine the shunt resistance of the circuit when the multiplying power of the shunt is known.

Note that if shunt resistance R_{sh} is 1 ohm and meter resistance R_{m} is exactly 99 ohm and the meter shows full scale deflection for a coil current I_{m} = 0.1 mA.

Then, the scale should be calibrated as 100 × 0.1 mA = 10 mA to read at full scale.

### Temperature compensation

The moving coil in a PMMC instrument is wound with thin copper wire whose resistance changes with change in temperature.

The errors are introduced in current measurements due to heating effect of the coil current which produces resistance change.

A **swamping resistance** made of manganin or constantan with negligible temperature coefficient having resistance 20 to 30 times the coil resistance is connected in series with the coil and shunt resistance made of manganin is connected in parallel to the combination in order to avoid resistance changes with temperature.

Therefore, the current I flowing through the circuit divides in proportion between the meter and the shunt which does not change appreciably with change in temperature.