DC Ammeters

DC Ammeters

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

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

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

circuit diagram of DC ammeter

We have to place this DC ammeter in series with the branch of an electric circuit, where the DC current is to be measured. The voltage across the elements, which are connected in parallel is same. So, the voltage across shunt resistor, RshRsh and the voltage across galvanometer resistance, RmRm is same, since those two elements are connected in parallel in above circuit. Mathematically, it can be written as

IshRsh=ImRmIshRsh=ImRm

Rsh=ImRmIsh⇒Rsh=ImRmIsh (Equation 1)

The KCL equation at node 1 is

I+Ish+Im=0−I+Ish+Im=0
Ish=IIm⇒Ish=I−Im

Substitute the value of IshIsh in Equation 1.

Rsh=ImRmIImRsh=ImRmI−Im(Equation 2)

Take, ImIm as common in the denominator term, which is present in the right hand side of Equation 2

Rsh=ImRmIm(1Im1)Rsh=ImRmIm(1Im−1)

Rsh=RmIIm1⇒Rsh=RmIIm−1(Equation 3)

Where,

RshRsh is the shunt resistance

RmRm is the internal resistance of galvanometer

II is the total Direct Current that is to be measured

ImIm is the full scale deflection current

The ratio of total Direct Current that is to be measured, II and the full scale deflection current of the galvanometer, ImIm is known as multiplying factor, m. Mathematically, it can be represented as

m=IImm=IIm(Equation 4)

Rsh=Rmm1Rsh=Rmm−1(Equation 5)

We can find the value of shunt resistance by using either Equation 2 or Equation 5 based on the available data.

Multi Range DC Ammeter

In previous section, we discussed about DC ammeter which is obtained by placing a resistor in parallel with the PMMC galvanometer. This DC ammeter can be used to measure a particular range of Direct Currents.

If we want to use the DC ammeter for measuring the Direct Currents of multiple ranges, then we have to use multiple parallel resistors instead of single resistor and this entire combination of resistors is in parallel to the PMMC galvanometer. The circuit diagram of multi range DC ammeter is shown in below figure.

Circuit Diagram of Multi Range DC Ammeter

Place this multi range DC ammeter in series with the branch of an electric circuit, where the Direct Current of required range is to be measured. The desired range of currents is chosen by connecting the switch, s to the respective shunt resistor.

Let, m1,m2,m3m1,m2,m3 and m4m4 are the multiplying factors of DC ammeter when we consider the total Direct Currents to be measured as, I1,I2,I3I1,I2,I3 and I4I4 respectively. Following are the formulae corresponding to each multiplying factor.

m1=I1Imm1=I1Im
m2=I2Imm2=I2Im
m3=I3Imm3=I3Im
m4=I4Imm4=I4Im

In above circuit, there are four shunt resistorsRsh1,Rsh2,Rsh2Rsh1,Rsh2,Rsh2 and Rsh4Rsh4. Following are the formulae corresponding to these four resistors.

Rsh1=Rmm11Rsh1=Rmm1−1
Rsh2=Rmm21Rsh2=Rmm2−1
Rsh3=Rmm31Rsh3=Rmm3−1
Rsh4=Rmm41Rsh4=Rmm4−1

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