ENEE2304 – Circuit Analysis 1

Welcome to

ENEE2304
Circuit Analysis

Text Books/Refrences:
• Introduction to Electric Circuits, 9th edition, J.Svobada, R. Dorf , 2014
• Electric Circuits, 10th Edition by Nilsson/Riedel
 Outline ENEE234 – Circuit Analysis 2

Course Objectives
Analysis of DC circuits with different techniques.
• Analysis of transient circuits using differential equations
technique.
• Analysis of single and three-phase AC circuits using phasor
transforms
• Calculations of sinusoidal steady-state power in single and three-
phase AC circuits
• Analysis of AC circuits using Laplace transforms
• Analysis and design of passive filter circuits
• Analysis of two-port circuits
• Use software tools (Matlab/ Simulink or PSPICE) to analyze
various types of circuits.
Outline ENEE2304 – Circuit Analysis 3

Chapters Topic

1 Circuit elements and variables.

2
Simple resistive circuits.

3
Techniques of circuit analysis.

4
Natural and step responses of RL, RC, and RLC circuits.

5 AC steady state analysis using phasor and Laplace transforms

6 AC steady state power calculations

7 Balanced three-phase circuit analysis*

8 Passive filter circuits
9 Two Port Networks
Outline ENEE2304 – Circuit Analysis 4

Grading Policy

Quizzes, assignments and participation: 25%

Midterm Exam: 30%
Final Exam: 45%
Chapter 1 – Review : Circuit Variables 5

Chapter 1 – Review : Circuit Variables

Systems of Units
• Most engineering disciplines have to routinely deal with two
systems of units: US units and SI units
• Electrical engineering uses SI units almost exclusively
Chapter 1 – Review : Circuit Variables 6

SI System
• Recall that the SI system is a decimal system that uses prefixes as multipliers.
• Some common SI prefixes are listed below:
SI Prefixes
Multiplier Prefix name Symbol Example: Ohm’s Law (V = IR) will
10+12 tera T be introduced in Chapter 2 where:
+9
10 giga G
10+6 mega M V = voltage measured in volts, V
10+3 kilo k I = current measured in amperes, A
10-3 milli m R = resistance measured in ohms, 
10-6 micro 
10 -9
nano n and 1V = (1A)(1 )
-12
10 pico p
-15
10 femto f
A) if I = 50.0 nA and R = 40.0 k , calculate V

B) if R = 10.0 k  and V = 3.75 mV, calculate I

•Chapter 1 ENEE2304 – Circuit Analysis 10

Current – the rate of change of charge with respect to time

dq(t) coulombs
i(t)  in units of  Amperes, A (So 1A = 1 C/s)
dt second
Illustration: Current can be thought of as the amount of charge flowing
through a conductor (such as a wire) that crosses some plane over a specified
period of time.
I positive charge

negative charge

Direction of current: There are two conventions for describing the direction
of the current:
1) electron flow

2) conventional current flow

•Chapter 1 ENEE2304 – Circuit Analysis 11

Key relationships:
t t
dq(t)
i(t) 
dt
 q(t)   i(t)dt
-
  i(t)dt
0
 q(0)
•Chapter 1 ENEE2304 – Circuit Analysis 12

Voltage – change in energy with respect to charge

dW joules
v(t)  in units of  volts, V (so 1V = 1J/C )
dq coulomb

• voltage is also referred to as potential difference

• voltage should always be expressed with a polarity (+ and - terminals)

Polarity: voltage should always be expressed with a polarity (+ and - terminals)

+ -
12V -12V 12V
- +
Two equivalent representations of the Unclear
voltage across a circuit element
•Chapter 1 ENEE2304 – Circuit Analysis 16

Passive and Active Devices

Passive device – a device that dissipates (saves) energy. The energy is given off
as heat or light.
Examples of passive devices: resistors, inductors, and capacitors (to be
introduced later). Practical items like filaments in bulbs, burners on a stove,
etc., are essentially resistors so they are also passive devices. The burner on
your stove can only use energy - it can’t produce energy on its own.
Passive sign convention – current is shown entering the
positive terminal. Therefore, if the current direction is
known, then the voltage polarity is known, and vice versa.
+ V _
I
Passive Passive
Device Device

The voltage polarity is known from the current direction

or
the current direction is known from the voltage polarity
•Chapter 1 ENEE2304 – Circuit Analysis 17

Passive Sign Convention and Ohm’s Law

Ohm’s Law will be introduced in Chapter 2, but here it will be used briefly to
make a point about passive sign convention.

Ohm’s Law: V = IR (voltage = current x resistance)

This law describes how voltage and current are related for a resistor.
Since a resistor is a passive device, this formula requires that passive sign
convention be used.

Example: Calculate the voltage, V, across the resistor shown below.

_
V +
I = 2A

R = 10 
Answer
V=-20 V
•Chapter 1 ENEE2304 – Circuit Analysis 18

Active device – a device that is capable of delivering

(supplying) energy, but might use energy, such as
when a battery is being charged.
Examples of active devices: batteries, voltage
sources, and current sources (to be introduced later)
Active sign convention – current is shown leaving
the positive terminal. Therefore, if the current
direction is known, then the voltage polarity is known,
and vice versa.
•Chapter 1 ENEE2304 – Circuit Analysis 19

Power – the rate of change of energy with respect to time

dW joules
power  p(t)  in  watts, W (so 1 W = 1 J/s)
dt second
also
dW dW dq
p(t)     v  i in (volts)(amperes)  watts, W (so 1 W = 1 V·A)
dt dq dt

Notes:
• If voltage and current are shown using passive sign convention then p = vi
calculates power absorbed (or used or dissipated)
• If voltage and current are shown using active sign convention then p = vi
calculates power delivered (or generated or supplied)
• Power delivered = -(Power absorbed) for a given device – For example, if a
device is absorbing 20W then it is delivering -20W.
• Whenever power is calculated, it should be made clear whether it is absorbed
or delivered
•Chapter 1 ENEE2304 – Circuit Analysis 21

Power check: For any circuit the following relationship exists:

Pdel = Pabs

Example: Shown below is an illustration of using one car battery to “jump

start” another car battery. Perform a “power check.” (Calculate the power for
each battery.)
10A

+ 12V - - 12V +
Good car Weak car
battery battery
•Chapter 1 ENEE2304 – Circuit Analysis 23

Energy: W or w(t) = energy (in joules, where 1J = 1Ws )

t
dW
p(t) 
dt
so w(t)   p(t)dt
-

or w(t)   p(t)dt  w(0)

0
•Chapter 1 ENEE2304 – Circuit Analysis 24

Energy Cost
Electricity Utilities charge for the amount of energy that is used each month
(power is the rate at which the energy is used).
The unit of energy used on power bills is the kilowatt-hour, kWh.
1 kWh = (1000W)(3600 s) = 3600000 Ws = 3.6 MJ
A typical rate used for energy costs might be 0.6 NIS/ kWh (discuss)
If energy is used linearly, then
dW W
p(t)   so W  P(t)
dt t
Typical power rates for appliances:
Appliance Power Rating (W)
Air conditioner 860
Blow dryer 1300
Clock 2
Dishwasher 1200
Electric Dryer 4800
Microwave Oven 800
Television 150
Electric Water Heater 2500