MCT242: Electronic Instrumentation

Lecture 3:

DC & AC Circuit Analysis

Faculty of EngineeringFaculty of EngineeringFaculty of EngineeringFaculty of Engineering

Outline

• Voltage and Current

• Ohm’s Law

• Kirchoff’s laws

• Resistors – Series and Parallel

• Voltage Dividers

• Capacitors, Inductors and R-C circuits

Basic Electrical Circuit

Voltage Source

Higher electrical Potential

Light

Heat

Lower Electrical Potential

•Voltage – difference in potential energy, Current flows from regions of higher electrical

potential to regions of lower electrical potential.

•Electrical Energy only flows in a closed path – closed system

•DC (Direct Current) are those circuits with static or slowly varying values.

•AC (Alternating Current) signals are those with rapid change or regular periodic change

•source of these terms is a historical artifact

•Wires are considered ideal – no resistance to flow of electrical energy

•The filament wire in the light bulb is a resistor that converts energy to light and heat

Simple Analogy• Voltage is a measure of electrical potential energy (units are volts)

– You can think of it as potential energy like water in a reservoir at the top of a hill

– The lowest energy state in the circuit is called Ground – standing water at the bottom of the hill

• Current is the flow of electrons from a high energy state to a lower energy state (units are amperes)

– You can think of it as water flowing through pipes from the top to the bottom of a hill

• Resistance is like narrow parts of the pipe (units are ohms)

– The more constrictions that are put in series, the slower the flow rate

– Total flow capacity is divided among parallel paths but the water has the same energy at the top and bottom of each parallel path

• Capacitance is like a little tank along the way (units are farads)

– Water (and potential energy in the form of a charge) can accumulate in the tank

• Just as the water’s potential energy is converted to kinetic energy (velocity) as it moves down the hill, so is electrical energy converted into other forms of energy along the way (heat, light, mechanical energy)

• If you take this analogy too far, it breaks down, but it is a good place to start

Water Analogy

Tank at the

top of the hill

Tank at the Bottom

of the Hill (Ground)

A voltage source

Is like a pump moving

water from low

potential energy (low

altitude) to higher

potential energy

(higher altitude)

Resistors are like pipes

Capacitors are like little

tanks along the way

Current Definitions

• Current is defined as flowing from higher potential energy to

lower potential energy

• This is often expressed as flow from + to –

• This convention existed before the discovery of the electron,

the basic atomic unit that carries electrical energy

• Electrons are negatively charged, so they actually flow from –

to +, the opposite of current

• In almost all applications, we use the concept of current as

our model/reference system

• Current is almost always represented by the variable I (i)

Voltage Sources – Series and Parallel

• In series, voltage sources add to increase voltage with no increase in current capacity

– Actual current may rise as voltage rises with a fixed resistive load

• In parallel, voltage sources do not increase voltage but they do increase the current capacity

– Exactly predicting the voltages requires a current loop analysis

1.5V

1.5V

1.5V1.5V

+

-

+

-3 volts

1.5 Volts

Kirchoff’s Laws

• Voltage– The sum of voltage drops and rises around

any path in a circuit in a closed path (start and end at the same point) must equal zero

– Since the voltage at any point in a circuit is an electrical energy potential, any path around the circuit must end up at the same energy potential or else the law of conservation of energy would be violated

• Current– The sum of all the current entering a node

of a circuit and leaving the node of a circuit must equal zero

• Since current is just the flow of electrons and electrons have an energy state and mass this is just a restatement of the laws of conservation of energy and conservation of mass

V

R

R

I

-.5V

-.5V

+V

i3 out = i1 + i2

i1 in

i2 in

Ohm’s Law• Voltage = Current x Resistance

• V = voltage, I = current, R = resistance

• V= IR, I = V/R, R = V/I – if you know 2 can calculate the third

• Almost every measuring circuit in this course will use this relationship

AA Battery

1.5 Volts1 KiloOhm resistor

Also called the Load

Current I = 1.5 Volts/1000 Ohms = .0015 amperes = 1.5 milliamps

Ω

+

-

Symbol for resistor

1.5 Volts

0 Volts

Short Circuits and Open Circuits

• A short circuit is when the + and – of a voltage source are directly connected with zero or essentially zero resistance

– A wire or a piece of metal can do this

– Due to Ohm’s law, when R is zero or near zero then current goes to infinity (V/R=I)

– This results in rapid heating and overloading the voltage supply

• An open circuit is when the + and – of a voltage source are not connected or connected by a very high resistance (> 100 Megaohms)

– In this case no current flows

Voltage Sources In Series and Parallel

Load

tot

Loadtot

R

VI

IRVVV

=

=+= 21

1.5V

1.5V

+

-

+

-

1.5V1.5V

R

Load

R

Load

I

Vtot

V1

V2

I1 I2

Itot

V1 V2Load

tot

Load

R

VIII

RIIVV

max21

2121 )(

=+=

+==Vmax

For parallel sources, Vmax is the highest of the two voltages. Exactly predicting the

voltages requires a current loop analysis

Property of material

Resistors – Series • Resistors in series add

• This type of circuit is a voltage divider – if resistors are equal the intermediate voltage will be half

V1

R1

R2 V3

Vtot

I

V2

)(

)(

)(

21

213

23

21

1

211

1

321

21

RR

RVV

IRV

RR

VI

RRIV

IRV

VVV

RRR

tot

tot

+=

=

+=

+=

=

+=

+=

Resistors - Parallel

• Resistors in parallel – add inverse

• This type of circuit is a current divider – if

resistances are equal, current down one leg is

half of the current of a single resistor

V R1 R2I1 I2

Itottot

tot

tot

R

V

R

V

R

VI

III

=+=

+=

21

21

V V

21

21

21

2

1...

111

RR

RRRtot

n

RRRR ntot

+=

=

++=

Voltage divider as the basis for instrumentation

Circuits• For all resistive sensors, the voltage divider is the primary circuit used in

instrumentation– Resistive sensors are those whose resistance value changes with

change in the measured quantity – e.g. Resistance Temperature Detector (RTD) resistance changes with

temperature, Strain Gage resistance changes with strain)

Known Resistor

(Rknown)

Resistive Sensor

(Rsensor)

Known

Voltage

(V1)

Voltage

Measurement

Proportional To

Sensor Value (V2)

)( 21

2

12

VV

RVeTemperaturR

RR

RVV

knownsensor

sensorknown

sensor

−=∝

+=

Sensors for Current• Two types of sensors are used for current- Ammeters

– A shunt – which is a precision very low resistance resistor over which a

voltage drop is observed

• Typically large blocks of metal to dissipate heat

• Must cause minimum additional voltage drop – typically 50-100

millivolts

– A clamp

• An inductive sensor which surrounds a wire converting the

electromagnetic field into a small AC current that can be read by a

smaller meter with a shunt

• Current through only one conductor is measured

– If put both in the meter, they cancel out

Use of Digital Multi Meter (DMM)

• To measure voltage (voltmeter function), measure ACROSS the load

– In parallel with the load

• To measure current (ammeter function), you have to measure through the load

– In series with the load

• To measure resistance (ohmmeter function), the circuit must be unpowered and then measure across the load

– You may have to remove the component to get an accurate reading as there may be other paths through the circuit that the ohmmeter function will measure

Load DMM

+

-

Using DMM as

voltmeter or

ohmmeter

DMM

+

-

Using DMM as ammeter

Resistor Color Code

Color 1st and 2nd Band 3rd Band

Black 0 x 1

Brown 1 x10

Red 2 x100

Orange 3 x1000

Yellow 4 x10,000

Green 5 x100,000

Blue 6 x1,000,000

Violet 7 x10,000,000

Gray 8 x100,000,000

White 9 x1,000,000,000

DC Power

• Power = Voltage x Current = VI• Since V=IR (Ohms Law), Power also = I^2R for purely

resistive direct current circuits– Direct current (DC) – where there is no periodic

change in voltage or current– Alternating current (AC) – where there is periodic

change in frequency and current• Power is in watts• A 9V battery with a 1000 ohm resistor (1 kilo-ohm)

across the terminals will have .009 amps running through it which will generate .081 watts

• A 9V battery with a 10 ohm resistor across it will have .9 amps which will generate 8.1 watts

Capacitors and Inductors• Capacitors store electrical energy in static charge

– Current is a function of the change in voltage with respect

to time

– Often made by a dielectric between two parallel plates

• Inductors store electrical energy in an electromagnetic field

– Voltage is a function of the change in current

– Often implemented by a coil of wire

Symbol for inductorSymbol for capacitor

Introduction To Capacitors• Capacitance of a device made from

two parallel plates separated by a dielectric is

– The dielectric constant times the area of the plate divided by the distance between the plates

– Capacitance is larger as the area of the plates increases and is smaller as the distance between the plates increases

– Capacitance measured in FARADS which are very large units of measure.

– Most electronic circuits uses capacitances in the micro-farad to picofarad range

– Most batteries are just special capacitors Energy stored in a capacitor

• One half of the capacitance times the voltage squared 2

2CV

E =

D

AC

ε=

Symbol for capacitor

Capacitors

• Can act as integrators and ac

filters

• Can act as differentiators and

DC blocks

R

C

C

R

Alternate

Symbol

for

capacitor

RC Circuit

• Is like filling a closed tank, current keeps flowing until the tank is full, and then it stops flowing

• Labview VI simulates and predicts this

AA Battery

1.5 Volts 1 KiloOhm

resistorΩ

1 microfarad

capacitor

Charge-Discharge of a 1 microfarad capacitor with a 1 MegaOhm resistor

Discharge initiated at t=2000 msec