Download Ohm`s Law, Resistance, Power and Energy

Lesson 2: Resistance
and Ohm’s Law
Learning Objectives
 Describe the concept of resistance.

Given a color code table, determine the value and
tolerance of fixed resistors using their color codes.

Use Ohm’s law to calculate current, voltage, and
resistance values in a circuit.
Discuss the difference between an open circuit and a
short circuit.
Demonstrate how to measure current, voltage, and
resistance in a circuit.


Resistance of conductors

Resistance is the opposition to charge movement.

As electrons move through a material, they constantly
collide with atoms in the material and with other
electrons.

These collisions cause some of the energy carried by the
charge to be released as heat.

So resistance is dependent on type of material, length
of the conductor, cross-sectional area and
temperature.
Resistance of conductors





Type of material: Atomic differences of materials
cause variations in how electron collisions affect
resistance
Differences produce resistivity.
The higher the resistivity, the greater is the
resistance of the conductor.
Represented by the symbol  (Greek letter rho)
Units of : Ohms x meters (Ω∙m)
Resistance of conductors
Length of conductor: Directly proportional to its length.
The longer the conductor, the greater is the resistance.
 If
you double the length of the wire, the resistance will
double

= length
 In
meters or feet
Resistance of conductors

Cross-sectional area:
 Inversely
proportional to cross-sectional area of the
conductor. The greater the area of the conductor, the
less is the resistance.
 If cross-sectional area is doubled, resistance will be
one half as much
 A =Cross-sectional area, in m2
Resistance of conductors



Temperature: for most conductors, a
temperature increase causes an increase in
resistance.
Increase is relatively linear
In semiconductors and insulators, increase in
temperature results in decrease in resistance
Resistance of conductors

Resistance of a conductor at a given temperature can be
expressed mathematically
R

A
where
[ohms, ]
  resistivity, in ohm-meters (  m)
 length, in meters (m)
A  cross-sectional area (m 2 )
1x10-3 inches = 1 mil
&
A(CM)
ACM = (diametermils)2
Example Problem 1

Need to measure length of this copper coil but don’t
want to unroll. Resistance measured is 103.7 Ohms.
Diameter is 0.01 inches
R

A
copper  10.37CM   / ft
1x10-3 inches = 1 mil
&
ACM = (diametermils)2
Fixed resistors
To provide control of electrical circuits.
Variable resistors

Variable resistors have an adjustable value of
resistance and have two principle functions
 Potentiometers
are used to adjust voltage.
 Rheostats are used to adjust current.
 Used to adjust volume, set level of lighting, adjust
temperature,…
a
Rab
b
Rbc
c
Resistor color coding
Resistors usually have 4, 5 or 6 color bands.
4 color bands:
5 color bands:
Band 1: First Digit
Band 1: First Digit
Band 2: Second Digit
Band 2: Second Digit
Band 3: Multiplier (10X)
Band 3: Third Digit
Band 4: Tolerance
Band 4: Multiplier (10X)
Band 5: Tolerance
Sometimes a 5th or 6th band is added (Reliability) to meet MILSPEC
requirements.
Resistor color coding
Read left
To right
MULTIPLIER
4=104
5=105
IF THIRD
BAND
Example Problem 2
Determine the resistance of a carbon resistors
having the color codes shown in the figure below.
Brown = 1
10 x 10 = 100 Ω
Black = 0
Brown = 10X
Gold = 5% tolerance = ± 5 Ω
Green = 5
565 x 10k = 56.5 MΩ
Blue = 6
Yellow = 4
Green = 100000X
Silver = 10% tol = ±5.6 MΩ
OHM’S LAW

Every conversion of energy from one
form to another can be related to this
equation.

In electric circuits, the effect we are
trying to establish is the flow of charge,
or current.

The potential difference, or voltage,
between two points is the cause
(“pressure”), and the opposition is the
resistance encountered.
Ohm’s law

Ohm discovered experimentally that voltage and
current in a wire were linearly related to each
other by a constant (Resistance)
E  IR [volts, V]
where
E is voltage in volts,
R is resistance in ohms,
I is current in amperes.

Current in a resistive circuit
 Directly
proportional to its applied voltage
 Inversely proportional to its resistance
Ohm’s law

Two different symbols are commonly used to
represent voltage.
E
for sources
 V for loads (such as the voltage drop across a resistor)
OHM’S LAW



In summary, therefore, the absence of an applied
“pressure” such as voltage in an electric circuit will result
in no reaction in the system and no current in the electric
circuit.
Current is a reaction to the applied voltage and not the
factor that gets the system in motion.
EXAMPLE: The greater the pressure in a hose, the
greater is the rate of water flow through the hose, just as
applying a higher voltage to the same circuit results in a
higher current.
Example Problem 3
Determine the current provided by the source.
I
Open circuits



Current can only exist where there is a
conductive path.
Since current is zero, the circuit has an infinite
resistance.
This is called an open circuit.
E E
R     ohms
I 0
Short circuits



A very low (or near zero) resistance is placed across a
circuit
Since resistance is near zero, all current will bypass the
rest of circuit and go through the short.
With zero resistance, current draw will approach the
limits of the power source (infinite current), frequently
causing damage to wiring or the power source
E E
I     amps
R 0
Measuring voltage



Voltage and current is measured using voltmeters and
ammeters, or a Digital Multi-Meter (DMM).
Measure voltage by placing the voltmeter leads across
the component whose voltage you wish to measure.
Polarity can be determined by probe placement.
“Auto-polarity”
Meter Symbol: Voltmeter
Current representation

The current depicted in the following circuits is
identical.
Measuring current


The current that you wish to measure must pass
through the meter.
Be careful that the meter’s maximum current
rating is not exceeded!
Meter Symbol: Ammeter
Voltage polarity and current direction



For the voltage across a resistor, always place the plus
sign at the tail of the current reference arrow.
To ensure the correct voltage sign on the DMM, place
the red lead where you think the “+” sign should be
For correct current polarity, the current should enter the
red lead of the DMM.
Measuring resistance


An ohmmeter is a device used to measure the
resistance of a component.
Resistance cannot be measured when voltage is
supplied to the circuit.
Measuring component resistance

You must isolate the component
that you are measuring from the
circuit!
Measuring Total Resistance

You must remove the power
source prior to measuring total
resistance!
Lesson 3: Power, and
Energy
Learning Objectives

Describe the relationship between battery
capacity, current drain and battery’s useful life.

Calculate the total cost given a rate of energy
consumption.

Calculate power supplied/dissipated in a circuit.

Calculate the power efficiency of a circuit.
POWER

In general, the term power is applied to
provide an indication of how much work
(energy conversion) can be accomplished
in a specified amount of time; that is,
power is a rate of doing work.
Power

Power is defined as the rate of doing work or as
the rate of energy transfer.
W
P
t


[watts, W]
The SI unit of power is the watt (W) or joules per
second.
The English unit of power is horsepower (hp).
1 hp  746 watts
Power in electrical systems

We need to express power in terms of voltage
and current, recall that
W
voltage V 
[joules/coulomb, J/C]
Q
Q
current I 
[coulomb/sec, C/sec]
t

Combining them we have
P
W W Q
   VI [watts, W]
t
Q t
Power in electrical systems

Applying Ohm’s law (V = IR and I = V/R) we can
also express power as
P  VI   IR  I  I 2 R [watts, W]
V  V
P  VI  V   
R R
2
[watts, W]
Power
Calculate the power to the heater using all three
electrical formulas
Power





Power is defined as the rate of doing work or as
the rate of energy transfer.
The greater the power rating of a light, the more
light energy it can produce each second
The greater the power rating of a heater, the
more heat energy it can produce
The greater the power rating of a motor, the
more mechanical work it can do per second
Power is related to energy. Is the capacity to do
work
Example Problem 1
A resistor draws 3 amps from a 12V battery. How
much power does the battery deliver to the
resistor?
I=3A
E=12V
ENERGY


For power, which is the rate of doing work,
to produce an energy conversion of any
form, it must be used over a period of time.
The energy (W) lost or gained by any
system is therefore determined by:
Energy

We can rearrange our formula for power
to solve for energy
work (or energy)  power  time

The unit of energy is joules (J), but is also expressed as
watt-hours (Wh) or kilowatt-hours (kWh).

Cost = Power × time × cost per unit

The residential energy cost from BGE is 14.8 cents per
kWh.
Energy
Cost = Energy × cost per unit
or
Cost = Power × time × cost per unit
Example Problem 2
Suppose you are at home and use 3 100-W lamps for 3
hours and An Xbox 500W for 2,5 hours. The TV consumes
180 W. At $0.148 per kilowatt-hour, how much will this cost
you?
Efficiency


In the process of converting energy, energy
losses inevitably occur.
The measure of output energy (or power) to
input energy (or power) is called efficiency.
Thermal
energy out
Efficiency
Poor efficiency in energy transfers results
in wasted energy
 An inefficient piece of equipment
generates more heat. As heat must be
removed to guarantee a proper function, it
means more $$.

Efficiency

Efficiency is usually expressed in percent and
denoted by the symbol .
Pout

 100%
Pin
Wout

 100%
Win

Since Pin = Pout + Plosses, efficiency can also be
expressed as
Pout

100%
Pout  Plosses
Efficiency

To find the total efficiency of a system
 Obtain
product of individual efficiencies of all
subsystems:
Total = 1 × 2 × 3 × ∙∙∙
Efficiency

Suppose a power amplifier delivers 400
W to its speaker system. If the power loss
is 509 W, what is the efficiency?
Example Problem 3
A 120 V dc motor drives a pump through a gearbox. The power
output to the pump is 1100 W. Gearbox efficiency is 75%.
Power input to the motor is 1600W.
What is Overall efficiency? Hp output and efficiency of the motor?