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Electric Circuits
1-1
1. Introduction
1-1 Overview
 Electrical and Electronics Systems

Produce, transmit, and measure electric signals
 Electrical systems

Communications systems

Computer systems

Signal-processing systems

Control systems

Power systems
 Electric circuit is a mathematical model that
approximates the behavior of an actual electrical
system
1-2 Basic Concept
1.2.1 Charge
 Charge

is a fundamental property of electrical phenomena

is described in positive and negative charges

is designated by the symbol q, measured in units of coulombs(C).

is the magnitude of the charge on a single electron.
1 C = 6.24 × 1018 electron

a single individual electron is −1.602 × 10−19 C
 Separation of charge creates an electric force (voltage)
 Motion of charge creates an electric fluid (current)
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Introduction to Electrical Engineering
1.2.2 The Force Between Two Charges
 𝐹=𝑘
𝑞1 𝑞2
𝑑2
where 𝑞1 is the charge at position 1
𝑞2 is the charge at position 2
d is the distance between the charge
k is a constant of 8.99 × 109 netwon meter 2 /C2
 Example 1.1
𝑞1 = 0.5𝐶 𝑞2 = −0.03𝐶 𝑎𝑛𝑑 𝐹 = 1𝑁
𝑑 = √𝑘
𝑞1 𝑞2
0.5 × 0.03
= √8.99 × 109
= 11,612 𝑚
𝐹
1
1.2.3 Conductors and Insulators
 Materials through which charge flows readily are called conductors.
 Insulators are materials that do not allow charge to move easily.
1.2.4 Current and Voltage
 Current (i)

is charge in motion

is measured in amperes (A)

is defined as 𝑖 =
𝑑𝑞
𝑑𝑡
where i=the current in amperes,
q=the charge in coulombs,
t= the time in seconds
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Electric Circuits
 Sign convention
positive current will be defined as the net rate of flow of positive charge.
 The range of currents
 Fluid Analogy
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1-3
Introduction to Electrical Engineering
 Voltage

is the energy per unit charge created by the separation

is measured in joules per coulomb

is defined as
where
𝑣=
𝑑𝑤
𝑑𝑞
v = the voltage in volts
w = the energy in joules
q = the charge in coulombs
 Simple fluid and electric circuit
 Example 1.6
dw = vdq
𝑤 = ∫ 𝑑𝑤 = 𝑣 ∫ 𝑑𝑞 = 𝑣𝑞 = 1.5 × 0.5 = 0.75 𝑗𝑜𝑢𝑙𝑠
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Electric Circuits
1-5
 The range of voltage
1.2.5 DC, AC, Frequency and Spectra
 DC

stands for direct current

refer to current that is flowing in a wire continuously in one direction at a
specified value
 AC

means alternating current

current goes back and forth, reversing its direction many times per second.
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Introduction to Electrical Engineering
 Frequency (f)

The number of times the direction changes per second

Unit of frequency is Hertz (Hz)
 Frequency spectrum
1.2.6 Reference Directions and Polarities
 Voltage polarity relationships
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Electric Circuits
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 Voltage-current relationships for energy absorbed and energy supplied
1.2.7 Power
 Power

is the rate of energy flow

is defined as 𝑝 =
𝑑𝑤
𝑑𝑡
where p = the power in watts [W]
w = the energy in joules [J]
t = the time in seconds [s]

𝑝=
𝑑𝑤
𝑑𝑡
𝑑𝑤
𝑑𝑞
= [ 𝑑𝑞 ] [ 𝑑𝑡 ] = 𝑣𝑖
where v = the voltage in volts [V]
i = the current in amperes [A]
 Energy

The integral of power of time (stored, dissipated)

defined as 𝑤 = ∫𝑡 1 𝑝 𝑑𝑡 = ∫𝑡 1 𝑣𝑖 𝑑𝑡
𝑡
𝑡
2
2
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Introduction to Electrical Engineering
 Example 1.8
absorbing or supplying power
1.2.8 Modeling
 Lumped element circuit modeling
 active element (source)
 passive element: resistors, capacitors and inductors
1.2.9 Ideal Circuit Elements
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Electric Circuits
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1.2.10 Sources
 Independent Sources

The source is independent of any other voltage or current in the circuit

represented by circle
 Dependent source

The source has the output which is dependent upon some other voltages or
currents in the circuit.

Dependent source is also called the controlled source.

Diamond is used to represent a dependent source.
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Introduction to Electrical Engineering
 Summary of circuit element designations
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