Chapter 1
Engr228
Circuit Analysis
Dr Curtis Nelson
Chapter 1 Objectives
• Understand and be able to use SI units and the standard
prefixes for powers of 10.
• Know and be able to use the definitions of voltage and current.
• Know and be able to use the definitions of power and energy.
• Be able to use the passive sign convention to calculate the
power for an ideal basic circuit element given its voltage and
current characteristics.
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Engineering Problem Solving
• All engineers share a considerable amount of common
ground, particularly when it comes to problem solving.
• Circuit analysis has long been a traditional introduction to
the art of problem solving from an engineering
perspective.
The International System of Units (SI)
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Derived Units in SI
Standardized Prefixes to Signify Powers of 10
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Dimensional Analysis
Dimensional analysis can be used to aid the solution to a problem
by ensuring that the final units are correct
• Examples
– Find the number of seconds in a year
– Find the number of miles in a light year (the speed of light is 186,287.5
miles per second)
31,557,600 seconds/year
5,878,786,100,000 miles
Simple DC Circuit
Current
• Voltage
• Current
• Resistance
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Charge
• The symbol for charge is Q or q and the unit is coulomb (C).
• Charge is bipolar, meaning that electrical effects are described
in terms of positive and negative charges.
• Electric charge exists in discrete quantities, which are integral
multiples of the electronic charge ±1.6022×10-19 C.
• Electrical effects are attributed to both the separation of
charge, voltage, and charges in motion, current. In other
words, voltage is potential energy while current is kinetic
energy.
Current and Charge
Current is the rate of charge flow:
I = dq/dt
1 ampere = 1 coulomb/second
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Current and Charge
• Current (designated by I or i) is the rate of flow of charge.
• Current must be designated with both a direction and a
magnitude.
• These two currents are the same:
Current and Charge: I = dq/dt
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Types of Current
Voltage (V or v)
• Voltage is the measure of work required to move charge thru a
circuit element.
• The unit of voltage is volt (V) = Joule/Coulomb = J/C
• Unlike current, voltage can exist between a pair of terminals
whether a current is flowing or not, i.e., a battery
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Circuit Elements
• A circuit element most often has
two terminals (sometimes three or
more).
• The relationship between the
voltage v across the terminals and
the current i through the device
defines the circuit element model.
Passive Sign Convention
• Voltage and current can be either positive or negative,
depending on how you specify a reference. To be consistent,
we will adopt the Passive Sign Convention:
Whenever the reference direction for the current in an element is
in the direction of the reference voltage drop across the element,
use a positive sign in any expression that relates the voltage to
the current. Otherwise, use a negative sign.
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Interpretation of Reference Directions
Example of Voltage Polarities
• Voltage (V or v) across an
element requires both a
magnitude and a polarity.
• Example: (a)=(b), (c)=(d)
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Power and Energy
• Power is the time rate of expending or absorbing energy
P = dw/dt
where
p = the power in watts,
w = the energy in joules
t = the time in seconds
• From the definitions for current and voltage, power is also
P = VI
Power and the Passive Sign Convention
• Since voltage and current can be either positive or negative,
we use the passive sign convention to ensure that the sign
of power is correct.
• Power is positive if the reference direction for the current is
in the direction of the reference drop across the terminals of
an element.
• When power is positive, the element is absorbing power.
• When power is negative, the element is supplying power.
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Example: Power
How much power is absorbed by the three elements above?
Pa = + 6 W, Pb = +6 W, Pc = -20 W
(Note: (c) is actually supplying power)
Textbook Problem 2.20 Hayt 7E
• Determine which of the
five sources are being
charged (absorbing
positive power), and show
that the algebraic sum of
the five absorbed power
values is zero.
Source
2 V source
8 V source
-4 A source
10 V source
-3 A source
Absorbed Power
(2 V)(-2 A)
(8 V)(-2 A)
(10 V)[-(-4 A)]
(10 V)(-5 A)
(10 V)[-(-3 A)]
-4W
- 16 W
40 W
- 50 W
30 W
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Chapter 1 Summary
•
•
•
•
Defined SI units and the standard prefixes for powers of 10.
Defined voltage and current.
Defined power and energy.
Explained the passive sign convention and used it to
calculate the power for an ideal basic circuit element given
its voltage and current.
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