# DC ammeters

Electronic measuring instruments 2020-11-20 00:14:00# DC ammeters

Current is the flow rate of the electric charge. If this electric charge only flows in one direction, the resulting current is called direct current (DC). The instrument, which is used to measure direct current called ** DC ammeter **.

If we place a resistor in parallel with the Permanent Magnet Moving Coil Galvanometer (PMMC), then the whole combination acts as a DC ammeter. Parallel resistance, which is used in DC ammeter, is also called shunt resistance or just ** shunt **. The value of this resistor should be considered small in order to measure the high value DC current.

The ** circuit diagram ** of the DC ammeter is shown in the figure below.

We have to place this ** DC ammeter ** in series with the branch of an electrical circuit, where the DC current is to be measured. The voltage across the elements connected in parallel is the same. Thus, the tension across the shunt resistor, $ R_ {sh} $ and the voltage across the galvanometer resistor, $ R_ {m} $ is the same, since these two elements are connected in parallel in the circuit above. ** Mathematically ** it can be written as follows:

$$ I_ {sh} R_ {sh} = I_ {m} R_ {m} $$

$ Rightarrow R_ {sh} = frac {I_ {m} R_ {m}} {I_ {sh}} $ (Equation 1)

The ** KCL equation ** at node 1 is

$$ - I + I_ {sh} + I_ {m} = 0 $$

$$ Right arrow I_ {sh} = I-I_ {m} $$

** Replace ** value of $ I_ {sh} $ in equation 1.

$ R_ {sh} = frac {I_ {m} R_ {m}} { I-I_ {m}} $ (Equation 2)

Let us take, $ I_ {m} $ as current in the denominator term, which is present in the right side of equation 2

$$ R_ {sh} = frac {I_ {m} R_ {m}} {I_ {m} (frac {1 } {I_ {m}} - 1)} $$

$ Rightarrow R_ {sh} = frac {R_ {m}} {frac {I} {I_ {m }} - 1} $ (equation 3)

Where,

$ R_ {sh} $ is the shunt resistance

$ R_ {m} $ is the internal resistance of the galvanometer

$ I $ is the total direct current to be measured

$ I_ {m} $ is the full scale deviation current

The ratio of the total direct current i.e. to be measured, $ I $ and the full scale deviation current of the galvanometer, $ I_ {m} $ is called ** multiplying factor, m **. Mathematically, it can be represented by

$ m = frac {I} {I_ {m}} $ (Equation 4)

$ R_ {sh} = frac {R_ {m}} {m-1} $ (Equation 5)

We can find the ** value of the shunt resistor ** using equation 2 or equation 5 based on available data.

## Multi-range DC ammeter

In the previous section, we discussed the DC ammeter obtained by placing a resistor in parallel with the PMMC galvanometer. This DC ammeter can be used to measure a ** particular range ** of forward currents.

If we want to use the DC ammeter to measure forward currents of ** multiple ranges **, then we have to use multiple parallel resistors instead of just one resistor and all that combination of resistors is in parallel with the PMMC galvanometer. The ** electrical diagram ** of the multi-range DC ammeter is shown below.

Place this multi-range DC ammeter in series with the branch of an electrical circuit, where direct current is required the range is to be measured. desired current is selected by connecting the switch, s to the respective shunt resistor.

Either, $ m_ {1}, m_ {2}, m_ {3} $ and $ m_ {4} $ are the **multiplier factors ** of the DC ammeter when considering the total direct current ents to be measured respectively as $ I_ {1}, I_ {2}, I_ {3} $ and $ I_ {4} $ . Here are the formulas corresponding to each multiplying factor.

$$ m_ {1} = frac {I_ {1}} {I_ {m}} $$

$$ m_ {2} = frac {I_ {2}} {I_ {m}} $$

$$ m_ {3} = frac {I_ {3}} {I_ {m}} $$

$$ m_ {4} = frac {I_ {4}} {I_ {m}} $$

In the above circuit, there are four ** shunt resistors **, $ R_ {sh1}, R_ {sh2}, R_ {sh2} $ and $ R_ {sh4} $. Here are the formulas corresponding to these four resistances.

$$ R_ {sh1} = frac {R_ {m}} {m_ {1} -1} $$

$$ R_ {sh2} = frac {R_ {m }} {m_ {2} -1} $$

$$ R_ {sh3} = frac {R_ {m}} {m_ {3} -1} $$

$$ R_ {sh4} = frac {R_ {m}} {m_ {4} -1} $$

The above formulas will help us find the resistance values of each shunt resistor.