EKT212/4 - PRINCIPLE OF MEASUREMENTAND INSTRUMENTATION

Current Measurement

Semester IIAcademic session 2016/2017

School of Computer and Communication EngineeringUniversiti Malaysia Perlis (UniMAP)

Email: said@unimap.edu.my

Outline

AmmeterPrinciple of OperationDesign

DC AmmeterMulti-range AmmeterThe Aryton Shunt

Insertion Effects

AmmeterIntroduction

I Ammeter is an instrument for measuring the electric currentin amperes in a branch of an electric circuit.

I It must be connected in series with the measured branch.

I It must have very low resistance to avoid significantalteration to the value of the current to be measured.

I Connecting an ammeter in parallel could damage the meter.

AmmeterPrinciple of Operation

I Earliest design is the D’Arsonval galvanometer or movingcoil ammeter (respond to DC only).

I It uses magnetic deflection, where current passing through acoil causes the coil to move in a magnetic field. E.g. PMMC.

I The voltage drop across the coil is kept to a minimum tominimize resistance across the ammeter in any circuit intowhich the it is inserted.

I Moving iron ammeter use a piece or pieces of iron whichmove when acted upon by the electromagnetic force of a fixedcoil of (usually heavy gauge) wire which respond to both DCand AC).

AmmeterDesign

AmmeterDesign ...continued

I Ammeter is placed in series with a circuit element to measurethe electric current flow through it.

I Meter must be designed to offer very low resistance to thecurrent so that it does not appreciably change the circuit it ismeasuring.

I To accomplish this, a small resistor is placed in parallel withthe galvanometer to shunt most of the current around thegalvanometer.

I Its value is chosen so that when the design current flowsthrough the meter it will deflect to its full-scale reading.

I A galvanometer full-scale current is very small: on the orderof mA.

DC Ammeter

I Figure shows a D’Arsonval meter movement in ammeter.I Rsh = resistance of the shuntI Rm = internal resistance of the meter movement (resistance

of the moving coil)I Ish = current through the shuntI Im = full-scale deflection current of the meter movementI I = full-scale deflection current for the ammeter

DC Ammeter

I The voltage drop across the meter movement is

Vm = ImRm

I The shunt resistor is parallel with the meter movement, thusthe voltage drop for both is equal,

Vsh = Vm

I Then the current through the shunt is

Ish = I − Im

I By using Ohms law, Then we can get shunt resistor as

Rsh =Vsh

Ish=

ImRm

Ish=

ImI − Im

Rm

DC AmmeterEXAMPLE

Calculate the value of the shunt resistance required to convert a1mA meter movement, with a 100Ω internal resistance, into a 0to 10mA ammeter.

Given that, Rm = 100Ω, Im = 1mA and I = 10mA,

Rsh =Im

I − ImRm =

1 × 10−3

(10 × 10−3) − (1 × 10−3)× 100 = 11.11Ω

The shunt resistance, Rsh is equal to 11.11Ω.

Multi-range Ammeter

I The current range in DC ammetercan be further extend by anumber of shunts.

I Range switch (typicallymulti-position switch) used toselect suitable shunts formeasurement.

I To protect the meter movement,multi-position withmake-before-break type switch isused.

I Operator is advised to startmeasurement with the highestcurrent range and graduallydecrease the range until good scaleis obtained.

Multi-range AmmeterEXAMPLE

Design a multi-range ammeter with range of 0 – 1A, 5A and10A employing individual shunt in each D’Arsonval movementwith an internal resistance of 500Ω and fsd of 10mA isavailable.

Given that, Rm = 500Ω and Im = 10mA,For the range of 0 – 1A, I = 1A;

Rsh1 =Im

I − ImRm =

10 × 10−3

(1000 × 10−3) − (10 × 10−3)×500 = 5.05Ω

Hence, the value for shunt resistances are given by,Rsh1 = 5.05Ω, Rsh2 = 1.002Ω and Rsh3 = 0.005Ω.

The Aryton Shunt

I The Aryton shunt eliminatesthe possibility of having themeter in the circuit withouta shunt.

I It can be used with a widerange of meter movements.

The Aryton Shunt

I The individual resistance values of the shunts are calculatedby starting with the most sensitive range and working towardthe least sensitive range.

Rsh = Ra + Rb + Rc

I The purpose of designing the shunt circuit is to allow measurecurrent, I that is some number n times larger than Im.

I The number n is called a multiplying factor and relates totalcurrent and meter current as

I = nIm

I Shunt resistance with n times larger than Im is

Rsh =Rm

n− 1

The Aryton ShuntAnalysis

Range switch at I1, henceI = I1; From the circuit,

(I1−Im)×(Rc+Rb+Ra) = ImRm

But,

Rsh = Rc + Rb + Ra

Therefore,

Rsh =Im

I1 − ImRm

The Aryton ShuntAnalysis ...continued

Range switch at I2,hence I = I2;

From the circuit,

(I2 − Im)(Rc + Rb) = Im(Rm + Ra)

I2(Rc + Rb) − Im(Rc + Rb) = ImRm + ImRa

(Rc + Rb) =Im(Rm + Rc + Rb + Ra)

I2

But,Rsh = Rc + Rb + Ra

Therefore,

(Rc + Rb) =ImI2

(Rm + Rsh)

The Aryton ShuntAnalysis ...continued

Range switch at I3, henceI = I3;

Analysis the circuit as previouslygives

Rc =ImI3

(Rm + Rsh)

where

Rsh = Rc + Rb + Ra

Insertion Effects

I Inserting an ammeter in a circuit always increases theresistance of the circuit and reduces the current in the circuit.

I This error caused by the meter depends on the relationshipbetween the value of resistance in the original circuit and thevalue of resistance in the ammeter.

I For high range ammeter, the internal resistance in theammeter is low.

I For low range ammeter, the internal resistance in the ammeteris high.

Insertion Effects...continued

Without ammeter;

Ie =E

R1

With ammeter;

Im =E

R1 + Rm

Insertion Effects...continued

I A ratio of Im and Ie is an error contributed by ammeterinsertion.

ImIe

=R1

R1 + Rm

I Hence, insertion error is given by

ei =

(1 − Im

Ie

)× 100%

Insertion EffectsEXERCISE

An ammeter with an internal resistance of 78Ω is used tomeasure the current through resistor Rc in figure below.Determine the percentage of error of the reading due toammeter insertion.