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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). To measure the Direct Current, we use instrument called DC ammeter.
Figure 2.3.1
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, Rsh and the voltage across galvanometer resistance, Rm is same, since those two elements are connected in parallel in above circuit.
Equations related to DC Ammeter
IshRsh = ImRm
Rsh = ImRm/Ish ( Eq.1)
The KCL equation at node 1 is
−I + Ish + Im = 0
Ish = I−Im
Substitute the value of Ish in Eq.1.
Rsh = ImRm/(I-Im) (Eq. 2)
Take, Im as common in the denominator term, which is present in the right-hand side of Eq. 2
Rsh = ImRm/[Im(1/(Im-1)]
Rsh = Rm/[I/(Im-1)] (Eq. 3)
Where,
Rsh = The shunt resistance
Rm = The internal resistance of galvanometer
I = The total Direct Current that is to be measured
Ish = Shunt current
Im = The full scale deflection current
The ratio of total Direct Current that is to be measured, I and the full scale deflection current of the galvanometer, Im is known as multiplying factor, m. The formula is,
m = I/Im (Eq.4)
Rsh = Rm/(m-1) (Eq. 5)
EXAMPLE 2.3.1
A 1mA meter movement with an internal resistance of 100Ω is to be converted into a 0-100 mA. Calculate the value of shunt resistance required.
Solution:
Rsh = (Im . Rm)/(I-Im)
Rsh = (1ma . 100Ω)/(100ma-1)
= 1.01 Ω
DC AMMETER (MULTI RANGE)
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.
Figure 2.3.2
Let, m1, m2, m3 and m4 be the multiplying factors of DC ammeter when we consider the total Direct Currents to be measured as, I1, I2, I3 and I4 respectively. Following are the formula corresponding to each multiplying factor.
m1 = I1/Im
m2 = I2/Im
m3 = I3/Im
m4 = I4/Im
In above circuit, there are four shunt resistors, Rsh1, Rsh2, Rsh3 and Rsh4. Following are the formula for the shunt resistors,
Rsh1 = Rm/(m1-1)
Rsh2 = Rm/(m2-1)
Rsh3 = R3/(m3-1)
Rsh4 = Rm/(m4-1)
EXAMPLE 2.3.2
Find shunt resistance for each ranges with ranges of 0-1A, 5A, 25A and 125A, employing individual shunts each. A D’Arsonval movement with an internal resistance of 730Ω and a full scale current of 5mA is available.
Solution:
Rsh = ImRm/(I-Im)
For 1A, For 5A,
Rsh = (5mA)(730Ω)/(1A-5mA) Rsh =(5mA)(730Ω)/(5A-5mA)
=3.668Ω = 730.73mΩ
For 25A, For 125A,
Rsh = (5mA)(730Ω )/(25A-5mA) Rsh = (5mA)(730Ω)/(125A-5mA)
= 146.03mΩ = 29.2mΩ
Figure 2.3.3
DC AMMETER (AYRTON SHUNT)
The Aryton shunt eliminates the pos¬sibility of having the meter in the cir¬cuit without a shunt. This advantage is gained at the price of slightly higher overall resistance. Figure shows a circuit of an Aryton shunt ammeter. The formula used based on the figure is,
Ish Rsh = Im Rm
In position 1, R1 is parallel with R2 + R3 + Rm
I1(R1) = Im ( R2 + R3 + Rm )
Where, I1 is the first range required.
In position 2, R1 + R2 is in parallel with R3 + Rm
I2(R1 + R2) = Im( R3 +Rm )
Where I2 is the second range required.
In position 3, R1 + R2 + R3 is in parallel with Rm.
I3( R1 + R2 + R3 ) = Im ( Rm )
EXAMPLE 2.3.3
Example: A PMMC instrument has a three-resistor Ayrton shunt connected across it to make an ammeter as shown in the figure. The resistance values are R1= 0.05 Ω, R2= 0.45 Ω and R3= 4.5 Ω. The meter has Rm= 1k Ω and FSD = 50 µA. Calculate the three ranges of the ammeter.
SOLUTION:
Switch at contact B:
Vs = ImRm = 50µA × 1kΩ = 50mV
Is = Vs/(R1+R2+R3) = 50mV/(0.05Ω+0.45Ω+4.5Ω) = 10mA
I = Im + Is = 50µA + 10mA
= 10.05mA
Switch at contact C
Vs = Im (Rm +R3) = 50µA(1kΩ +4.5kΩ) ᵙ 50mV
Is = Vs/(R1+R2) = 50mV/(0.05Ω+0.45Ω) = 100mA
I = Im + Is = 50µA + 100mA
= 100.05ma
Switch at contact D:
Vs = Im(Rm +R3 + R2) = 50µA(1kΩ +4.5kΩ +0.45Ω) ᵙ 50mV
Is =Vs/R1 = 50mV/(0.05Ω) =1A
I = Im + Is = 50µA + 1A
= 1.00005 A
Figure 2.3.4
DC Ammeter: Ayrton Shunt
REQUIREMENTS OF A SHUNT
1. Minimum Thermo Dielectric Voltage Drop
Soldering of joint should not cause a voltage drop.
2. Solderability
Resistance of different sizes and values must be soldered with minimum change in value. The following precautions should be observed when using an ammeter for measurement.
Ø Never connect an ammeter across a source of emf. Because of its low resistance it would draw a high current and destroy the movement. Always connect an ammeter in series with a load capable of limiting the current.
Ø Observe the correct polarity. Reverse polarity causes the meter to deflect against the mechanical stopper, which may damage the pointer.
Ø When using a multirange meter, first use the highest current range, then decrease the current range until substantial deflection is obtained. To increase the accuracy use the range that will give a reading as near full scale as possible.
How to use an ammeter:
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