EKT112:PRINCIPLES OF MEASUREMENT AND INSTRUMENTATION

Week 2:Voltage & Current Measurement

Introduction of electric circuitThe ultimate goal of the circuit theory is

topredict currents and voltages in complexcircuits (circuit analysis) and to design

electricalcircuits with desired properties. The

circuits are built with circuit elements. Some of

these elements (voltmeters, ammeters, wires,

resistors, capacitors, inductors, and switches) are described below.

Voltmeters and Ammeters

Electrical currents can be measured with an ammeter.

To measure the current in the wire shown in Fig. 1a, the wire should be cut and the ammeter should be inserted.

The current will flow through the ammeter (Fig. 1b).

Ammeters

Ammeters

An ideal ammeter should have a negligible effect on the circuit. This means that the voltage difference between its two terminals (A and B) should be zero.

In other words,the internal resistance (impedance) of an ideal ammeter is zero.

Voltmeter

Voltmeter

To measure voltage, the two terminals of a voltmeter should be connected to two points

in the circuit between which the potential difference is measured. An ideal voltmeter should not affect the circuit.

Therefore, current through the voltmeter (this is current in Fig.2) should be zero.

In other words, internal resistance (impedance) of an ideal voltmeter is infinity. A real voltmeter is never ideal and its impedance is finite.

Kirchhoff laws

Kirchhoff laws are applicable to both the linear and not linear circuits.

They provide a universal tool for circuit analysis.

Kirchhoff laws

Kirchhoff’s current law: The sum of the currents entering

a node is equal to the sum of currents leaving the node.

A node is a point where two or more wires are interconnected.

Kirchhoff laws

Kirchhoff’s voltage law: An algebraic sum of voltages

across all elements along any closed path is zero.

Algebraic sum means that we should take + sign if the voltage rises after a circuit element and “–“ sign if the voltage drops after a circuit element.

Kirchhoff laws (cont…)

Analysis of a circuit. General rules:1. Identify every loop which does not contain

another loop (such a loop is called mesh). Assign a current for every loop. The current direction can be chosen arbitrary. This step ensures that the Kirchhoff’s current law is automatically satisfied.

2. Use Ohm’s law (or other relations between voltages and currents if the circuit includes capacitors, inductors, diodes, etc) to calculate the voltage across all elements along every mesh and write equations (for every mesh) usingKirchhoff’s voltage law. Important! If two currents flow through an element, the currents should be added like vectors (their directions are important!).

3. Solve the equations.

Example

Example 2

Example 2

PART 2

EKT112PRINCIPLES OF MEASUREMENT AND INSTRUMENTATIONWEEKS 2-3

CURRENT, VOLTAGE & RESISTANCE MEASUREMENT

Topics Outline1.0 Device for Current Measurement

1.1 Analog ammeter1.2 Galvanometer

2.0 Device for Voltage Measurement2.1 Analog voltmeter2.2 Oscilloscope2.3 Potentiometer

3.0 Device for Resistance Measurement3.1 Ohmmeter3.2 Wheatstone bridge circuit

4.0 Digital Multimeter

Objective

As introduction to the student into some

basic measurement device for current,

voltage & resistance.

1.0CURRENT MEASUREMENT

Basic analog measurement of current –uses inductive force on the current carrying conductor in magnetic field.

This force can be used to measure the needle deflection on a display.

Direct Current (DC) Charges flow in one direction commonly found in many low-voltage applications,

especially where these are powered by batteries

Alternating Current (AC) Flow of electric charge changes direction regularly Example: audio & radio signal Home & school use AC

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Fig 1-1 The d’Arsonval meter movement

The basic moving coil system generally referred to as a d’Arsonval meter movement or Permanent Magnet Coil (PMMC) meter movement.

Current-sensitive device capable of directly measuring only very small currents.

Its usefulness as a measuring device is greatly increased with the proper external circuitry.

The D’Arsonval Meter Movement

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Current from a circuit in which measurements are being made with the meter passes through the windings of the moving coil. Current through the coil causes it to behave as an electromagnet with its own north and south poles. The poles of the electromagnet interact with the poles of the permanent magnet, causing the coil to rotate. The pointer deflects up scale whenever current flows in the proper direction in the coil. For this reason, all dc meter movements show polarity markings.

1.1 Ammeter An ammeter is an instrument for measuring the

electric current in amperes in a branch of an electric circuit.

It must be placed in series with the measured branch, and must have very low resistance to avoid significant alteration of the current it is to measure.

connecting an ammeter in parallel can damage the meter

Ammeter – Principle of Operation

The earliest design is the D'Arsonval galvanometer or moving coil ammeter (respond to ac only)

It uses magnetic deflection, where current passing through a coil causes the coil to move in a magnetic field

The voltage drop across the coil is kept to a minimum to minimize resistance across the ammeter in any circuit into which the it is inserted.

Moving iron ammeters use a piece or pieces of iron which move when acted upon by the electromagnetic force of a fixed coil of (usually heavy gauge) wire (which respond to both dc & ac)

Ammeter Design

An ammeter is placed in series with a circuit element to measure the electric current flow through it.

The meter must be designed offer very little resistance to the current so that it does not appreciably change the circuit it is measuring.

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

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

A galvanometer full-scale current is very small: on the order of milliamperes.

28

In most circuits, Ish >> Im

Fig. 1-2 D’Ársonval meter movement used in ammeter circuit

Basic DC Ammeter CircuitAmmeter

Where

Rsh = resistance of the shuntRm = internal resistance of the

meter movement (resistance of the moving coil)

Ish = current through the shunt Im = full-scale deflection current of

the meter movementI = full-scale deflection current for

the ammeter

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The voltage drop across the meter movement is

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

Then the current through the shunt is,

By using Ohm’s law

mmm RIV

msh VV

msh III

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Cont.Then we can get shunt resistor as

0.1..............mm RII

IR

I

I

I

RI

I

VR

m

m

sh

m

sh

mm

sh

shsh

Ohm

Example 1-1Calculate the value of the shunt resistance required to convert a 1-mA meter movement, with a 100-ohm internal resistance, into a 0- to 10-mA ammeter.

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Solution:

VmARIV mmm 1.01001

VVV msh 1.0

mAmAmAIII msh 9110

11.119

1.0

mA

V

I

VR

sh

shsh

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The Ayrton Shunt

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

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

We can get shunt resistance with n times larger than Im is

I = nIm

1

n

RR m

sh

………1.1

………1.3

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Examples 1-2

A 100 µA meter movement with an internal resistance of 800 Ω is used in a 0- to 100 mA ammeter. Find the value of the required shunt resistance.Answ: ~ 0.80 ohm

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Advantages of the Ayrton:

Fig 1-3 Ayrton shunt circuit

Eliminates the possibility of the meter movement being in the circuit without any shunt resistance.

May be used with a wide range of meter movements.

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Cont.

The individual resistance values of the shunts are calculated by starting with the most sensitive range and working toward the least sensitive range

The shunt resistance is

On this range the shunt resistance is equal to Rsh and can be computed by Eqn

cbash RRRR

1

n

RR m

sh

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Cont.

2

)(

I

RRIRR mshm

cb

3

)(

I

RRIR mshm

c

)( cbsha RRRR

ccbb RRRR )(

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Ammeter insertion effects

Inserting an ammeter in a circuit always increases the resistance of the circuit and reduces the current in the circuit. This error caused by the meter depends on the relationship between the value of resistance in the original circuit and the value of resistance in the ammeter.

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Cont.

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

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

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1R

EI e

Fig. 2-3: Expected current value in a series circuit

mm RR

EI

1

Fig 2-4: Series circuit with ammeter

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Cont.

hence;

me

m

RR

R

I

I

1

1

Therefore

%1001

e

m

I

IInsertion error =

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Example 1-3

A current meter that has an internal resistance of 78 ohms is used to measure the current through resistor Rc in Fig. 2.5. Determine the percentage of error of the reading due to ammeter insertion.

Fig. 2.5

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Solution:

The current meter will be connected into the circuit between points X and Y in the schematic in Fig. 2.6. When we look back into the circuit from terminals X and Y, we can express Thevenin’s equivalent resistance as

RTH = 1 k + 0.5 k = 1.5 k

ba

bacTH RR

RRRR

Fig. 2-6

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Cont.

Therefore, the ratio of meter current to expected current:

Im/Ie= 1.5 k/(1.5 k + 78) = 0.95

Solving for Im yields, Im = 0.95Ie

Insertion error = [1 – (Im/Ie)] x 100% = 5.0%

me

m

rR

R

I

I

1

1

1.2 Galvanometer

It is an electromechanical transducer that produces

a rotary deflection, through a limited arc, in response

to electric current flowing

through its coil.

Galvanometer has been applied to devices used in measuring, recording, and positioning equipment.

Galvanometer – Principle of Operation

Such devices are constructed with a small pivoting coil of wire in the field of a permanent magnet. The coil is attached to a thin pointer that traverses a calibrated scale. A tiny spring pulls the coil and pointer to the zero position.

In some meters, the magnetic field acts on a small piece of iron to perform the same effect as a spring. When a direct current (DC) flows through the coil, the coil generates a magnetic field.

This field acts with or against the permanent magnet. The coil pivots, pushing against the spring, and moving the pointer. The hand points at a scale indicating the electric current.

A useful meter generally contains some provision for damping the mechanical resonance of the moving coil and pointer so that the pointer position smoothly tracks the current without excess vibration.

Galvanometer – Application

Are used to position the pens of analog chart (example: electrocardiogram)