This document covers key concepts in circuit analysis including electric charge, current, potential (voltage), power, and energy. It defines current as the rate of positive charge flow and discusses examples. Voltage is defined as energy per unit charge and the passive sign convention for circuit elements is introduced. Power is defined as the rate of energy transfer and the passive sign convention for power is described. Electrical energy consumed is calculated as the product of power and time. Examples of calculating current, voltage, power, and energy in circuits are provided.

1. 1
EE216 CIRCUIT ANALYSIS I
Lecture # 2 – Chapter 1

2. 2
RECAP
 Electrical Engineering Overview
 5 classifications of Electrical Engineering
 Mathematical models – 3 assumptions for circuit
theory
 Engineering Design Flow and importance of Circuit
Analysis

3. 3
ELECTRIC CHARGE (COULOMB)
 Basis for all electrical activity
 Electrical effects are due to
 separation of charge -> electric force (voltage)
 charges in motion -> electric flow (current)
 Macroscopically, most matter is electrically neutral most
of the time.
 Exceptions: clouds in a thunderstorm, plates of a charged
capacitor, etc.
 Microscopically, matter is full of electric charges
 Electric charge exists in discrete quantities, integral multiples
of the electronic charge -1.6 x 10-19 Coulomb

4. 4
ELECTRIC CURRENT
 Definition: rate of positive charge flow
 Symbol: i
 Units: Coulombs per second ≡ Amperes (A)
 Note: Current has polarity. Direction of flow of current
(conventionally) is from positive to negative potential.
Though actual electronic current moves from negative to
positive potential.
i = dq/dt where
q = charge (Coulombs)
t = time (in seconds)
 Current cannot flow unless there is a
closed path and a stimulus to flow. André-Marie
Ampère's
1775-1836

5. 5
CURRENT EXAMPLE 1
 105 positively charged particles (each with a charge 1.6×10-19
C) flow to the right (+x direction) every nanosecond. How
much electric current is flowing?
 1A = 6.25 ×1018 electrons/second – huge unit of current

6. 6
CURRENT EXAMPLE 2
 105 electrons flow to the left (-x direction) every
microsecond. How much electric current is flowing?

7. 7
ELECTRIC POTENTIAL (VOLTAGE) 1/4
 Electromotive Force (EMF): The stimulus to cause a
current to flow in a circuit. (e.g. a battery or a generator).
 Potential Difference (or Voltage): An EMF source causes
different potential to exist in a circuit at two points
connected to it. This difference of potential causes a flow
of current.
 Voltage measured in Volts (V).

8. 8
ELECTRIC POTENTIAL (VOLTAGE) 2/4
 Reference: Voltage is measured with respect to a
reference. If not specified, the reference is taken to
be at 0 V and is termed as GROUND or less
frequently as EARTH. Why EARTH?
 Earth very good conductor – sigma low but area
huge.
o e.g. in past telephone companies used earth as return
conductor
 GROUND is equi-potential – electrically neutral.
8

9. 9
ELECTRIC POTENTIAL (VOLTAGE) 3/4
 Definition: energy per unit charge
 Symbol: v
 Units: Joules/Coulomb ≡ Volts (V)
v = dw/dq
where w = energy (in Joules),
q = charge (in Coulombs)
 Subscript convention:
Vab means the potential at a with reference to potential at b.
Vab ≡ Va - Vb

10. 10
ELECTRIC POTENTIAL (VOLTAGE) 4/4
 Conventions vary.
 Labels represent
voltages with
respect to ground.
 If any other
reference is
required, an arrow is
used to mark it. Or,
simply label it.

11. 11
VOLTAGE EXAMPLE 1
 Suppose you have an unlabelled battery and you measure its
voltage with a digital voltmeter (DVM). It will tell you the
magnitude and sign of the voltage.
With this circuit, what are you measuring?
vab
The DVM indicates −1.401 V.
Which is the positive battery terminal?
Since va is lower than vb by 1.401 V, node “b”
is +ve.
 Note that we have used the “ground” symbol ( ) for the
reference node on the DVM. Often it is labeled “C” for
“common.”

12. 12
VOLTAGE EXAMPLE 2
 Find vab, vca, vcb
 What is va?
 What is vcd?
 Note that the labeling convention has nothing to do with
whether or not v is positive or negative.

13. 13
THE IDEAL BASIC CIRCUIT ELEMENT
 Has 3 Attributes:
1. Two terminals (points of connection)
2. Mathematically described in terms of current and/or voltage
3. Cannot be subdivided into other elements
• Polarity reference for voltage can be indicated by
plus and minus signs
• Reference direction for the current is indicated by
an arrow
• Choice completely arbitrary
• Once choice made: Passive Sign Convention
“Whenever the reference direction for the current into an element
is in the direction of the reference voltage drop across the
element, use a +ve sign in any expression that relates the
voltage to the current, otherwise use a –ve sign.”

14. 14
REFERENCE DIRECTIONS
 A problem like “Find the current” or “Find the
voltage” is always accompanied by a definition of
the direction.
 In the circuit element below, if the current turns out
to be 1 mA flowing to the left, we would say:
i = -1 mA
 There is no need to initially guess the reference
direction so that the answers come out positive.

15. 15
ELECTRIC POWER & ENERGY
 Why Power?
 Definition: power is the transfer of energy per unit time
 Symbol: p
 Units: Joules per second ≡ Watts (W) [746 W = 1HP]
p = dw/dt = (dw/dq)(dq/dt) = vi
 Concept:
 As a positive charge q moves through a drop in voltage
v, it loses energy.
 One watt of power equals the work done in one second
in moving one coulomb of charge through one volt of
potential difference.
 Power not conveyed by positive or negative charges,
but by fields, electrons are just an envelope or guide for
that.
 Energy transfers at speed of light.
James Watt
1736 - 1819

16. 16
PASSIVE SIGN CONVENTION FOR POWER
Power p = vi Power p = -vi
 If p > 0, power is being delivered to the box.
“Whenever  If p < 0, the power reference is being direction extracted for the from current the box.
into an element
is in the direction of the reference voltage drop across the
element, use a +ve sign in any expression that relates the
voltage to the current, otherwise use a –ve sign.”

17. 17
POSITIVE OR NEGATIVE POWER?
 If p < 0, element is supplying or “generating” power.
 Positive charge flowing from lower to higher potential.
 How can a circuit element supply power?
 By converting
chemical/mechanical/solar/thermal/nuclear energy into
electrical energy or releasing stored energy.
 If p > 0, element is absorbing or consuming power.
 Positive charge is flowing from higher to lower potential.
 How can a circuit element absorb power?
 By converting electrical energy into heat (resistors in
toasters), light (light bulbs), or sound (speakers) or by
storing energy (e.g. charging a battery).

18. 18
POWER EXAMPLE
 Find the power absorbed by each element:
Conservation of energy
 Given the following parameter values:
total power delivered
equals
total power absorbed
vi (W)
- 918
- 810
- 12
400
224
1116

19. 19
ELECTRICAL ENERGY
o Electrical energy (or less commonly electrical work) is the
amount of power consumed in a given time.
w pt
o FESCO charges us for actual units of energy consumed.
o Unit of energy is Watt-hour (Wh). More commonly
Kilowatt-hour (KWh).
o 1 FESCO Unit = 1 KWh.

20. 20
ELECTRICAL ENERGY EXAMPLES
 An incandescent bulb of 100W consumes 1 Unit of
electricity in 10 hours.
 An energy saver of 30W consumes 1 Unit in 33.33
hours.
 A split air conditioner of 2 Tons (cooling capacity)
has a wattage of 2800W (2.8KW). This means in
one hour it will consume 2.8 Units!
Task #2:
Try finding out average bill per month of your
household by estimating the average use of all the
electric equipment considering their wattage in
your home. (Know that not all units consumed are
billed at the same rate.)