Chapter 04
Ohm’s Law, Power,
and Energy
C-C
Tsai
Source:
Circuit Analysis: Theory and Practice Delmar Cengage Learning
Ohm’s Law (published in 1827)

Current in a resistive circuit

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Directly proportional to its applied voltage
Inversely proportional to its resistance
I
E
R
Express all quantities in base units of volts,
ohms, and amps
Also expressed as E = IR and R = E /I
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Fixed Resistance for Ohm’s Law
Doubling voltage doubles the current
E
I
R
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Fixed Voltage for Ohm’s Law
Doubling resistance halves the current
E
I
R
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Examples for Ohm’s Law
Example 1
R=?
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Examples for Ohm’s Law
Example 2
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Examples for Ohm’s Law
Example 3
Show the current direction for each circuit
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Ohm’s Law in Graphical Form

Linear relationship between current and voltage
y = mx versus I = E / R = G E , where G = 1/R
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y is the current
x is the voltage
m is the slope
Slope (m) determined by resistance or conductance
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Open Circuits
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Current can only exist where there is a conductive
path
Open circuit: Occurs when there is no
conductive path
An open circuit has infinite resistance
If I = 0, Ohm’s Law gives
R = E /I = E / 0  infinity ∞
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Voltage Symbols

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Voltage source by E
Voltage drop at a load by V
V = IR , voltages often referred to as IR drops
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Example:
V1 = ?
V2 = ?
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Voltage Polarities
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Polarity of voltage drops across resistors is
important in circuit analysis
Drop is + to – in the direction of conventional
current
To show this, place plus sign at the tail of current
arrow
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Examples: Voltage Polarities
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Examples:
V=?
V=?
V=?
V=?
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Examples:
V=?
V=?
V=?
V=?
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Current Direction

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Current usually proceeds out of the positive
terminal of a voltage source
If the current is actually in this direction, it will
be supplying power to the circuit
If the current is in the opposite direction (going
into the positive terminal), it will be absorbing
power (like a resistor)
Notice that a negative current actually proceeds
in a direction opposite to the current arrow
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Current Direction

Notice that a negative current actually proceeds
in a direction opposite to the current arrow
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How to light LEDs
In forward direction, LED on, 10~20mA, 1.7V
 In reverse direction, LED off.
For example:
If E = 6V, determine R for lighting the LED.
If E =19V, determine R for lighting the LED.

R
E
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Power


Power is the rate of doing work
Power = Work / time
P =W / t
Power is measured in watts (W)
Work and energy measured in joules (J)
Power is related to energy
One watt = One joule per second
1W=1J/s

1 hp = 746 watts
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Power Applications
For example:

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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
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Power Conversion for Applications
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Power in Electrical Systems
From V = W /Q and I = Q / t, we get
P = VI
 From Ohm’s Law, we can also find that
P = I 2R and P = V 2/R
 Power is always in watts
 We should be able to use any of the power
equations to solve for V, I, or R if P is given
For example:
P
I 
R
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V 
PR
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Examples: Power in Electrical Systems
Example 1
P=?
Example 2
P1 = ? and P2 = ?
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Power Rating of Resistors
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Resistors must be able to safely dissipate
their heat without damage
Common power ratings of resistors are 1/8W,
1/4W, 1/2W, 1W, or 2W
Customary safety margin: two times the
expected power
An overheated resistor

Often the symptom of a problem rather than its cause
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Power Direction Convention
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Power Direction Convention for
Electric Vehicles
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Energy

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Energy = Power × time
W = P ×t
Units are joules, Watt-seconds, Watt-hours or
kilowatt-hours (kWh)
For multiple loads

Total energy is sum of the energy of individual
loads
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Watthour Meter
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Energy use is measured by
watthour meter in kilowatthours (kWh), by the power
company
Electromechanical devices

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Motor with speed proportional to
the load
Electronic meters perform
function electronically
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Display results on digital
readouts
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Energy in Cost
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Cost = Energy × cost per unit
or
Cost = Power × time × cost per unit
For example:
Find the cost of running a 2000-watt heater for
12 hours if electric energy costs $3 per kilowatthour:
Energy = 2000W × 12 h = 24kWh
Cost = $3/kWh × 24kWh = $ 72
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Law of Conservation of Energy
Energy can neither be created nor destroyed
 Converted from one form to another
Examples:
Electric energy into heat
Mechanical energy into electric energy
 Energy conversions
 Some energy may be dissipated as heat,
giving lower efficiency

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Efficiency

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Poor efficiency in energy transfers results in
wasted energy
An inefficient piece of equipment generates
more heat
Efficiency (in %) is represented by η
(Greek letter eta)

Pout
100%
Pin
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Efficiency

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Heat removal requires fans and heat sinks
Always less than (or equal to) 100%
Efficiencies vary greatly:
 Power transformers may have efficiencies
of up to 98%
 Some amplifiers have efficiencies below
50%
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Total Efficiency

To find the total efficiency of a system
Obtain product of individual efficiencies of all subsystems:
Total = 1 × 2 × 3 × ∙∙∙
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Example: Total Efficiency
Total =?
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Nonlinear and Dynamic
Resistances
Linear:
R =V / I
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Computer Analysis
Multism
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Computer Analysis
PSpice
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Computer Analysis
PSpice to measure the current
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Plotting Ohm’s Law
With fixed resistance,
the current is linear to the voltage
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Kernel abilities
1. What is Ohm’s law? Please give an example.
2. How to light a LED? Please give an example.
3. How to calculate the dissipated power on a resistor?
Please give an example.
4. How to estimate the power fee per month for a
family? Please give an example.
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Problem 12
If E=28V, what does the meter indicate?
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Problem
Solve the current I of the loop
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An Energy Problem
Given electric products that used per day as
below, what cost a family pay per month?
(NT$2.5 is for a kWh)
100W-Lamp 6 hours
300W-TV 5 hours
500W-Refrigenator 10 hours
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