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Engineering Practice
Electric Fitting
Resistance
• Electrical resistance is the ratio of
voltage drop across a resistor to
current flow through the resistor.
• Polarities are governed by the
passive sign convention.
v
R
i
R
i
+
v
-
I, V & R
Current = voltage / resistance
• I=V/R
V=IxR
Definitions
• Voltage = potential energy / unit charge, units
= Volts
• Current = charge flow rate, units = Amps
• Resistance = friction, units = Ohms
Example
• Voltage drop when current flows through
resistor
•
V1 - V2 = I R
V1
I
R
V2
Power Consumed by Resistors
• Resistors consume
power.
• v and i are both
positive or both
negative.
R
i
+
v
-
p  v i
v  R i
v
i
R
Creating a Circuit Model
• A circuit model is usually two or more circuit elements that
are connected.
• A circuit model may have active elements (sources) as well
as passive elements (such as resistors).
• By the assumption that electric signal propagation is
instantaneous in a circuit, our circuit model has lumped
parameters (A lumped system is one in which the
dependent variables of interest are a function of time alone.
In general, this will mean solving a set of ordinary
differential equations (ODEs)).
Schematics
• Symbols represent circuit elements
• Lines are wires
+
Resistor
Battery
Sample circuit
Ground
V
+
I
R
Ground voltage
defined = 0
Example of a Circuit
Model
1000 ft AWG 14
Copper Wire
100 W
Lamp
120 V Battery
0.25 
2.57 
144 
120 V
2.57 
Kirchhoff’s Voltage Law
• The sum of the voltage drops around a closed path is zero.
• Example: -120 + V1 + V2 + V3 + V4 = 0
0.25 
+ V1 -
2.57 
+ V2 -
120 V
2.57 
- V4 +
+
V3
-
144 
Kirchhoff’s Current Law
• A node is a point where two or more circuit elements are
connected together.
• The sum of currents associated with a node is zero.
I1
I4
I3
I2
Parallel And Series Resistors
Series circuit
V = R1 I + R2 I = Reff I
Reff = R1 + R2
Series
• Same current flows through all
Parallel
• Same voltage across all
R1
V
Parallel circuit
I = V/R1 + V/R2 = V/Reff
1/Reff = 1/R1 + 1/R2
+
I
R2
I
V
+
R1
I1
R2
I2
Note: these points are
connected together
Resistive voltage divider
• Series resistor circuit
• Reduce input voltage to desired level
• Advantages:
– simple and accurate
– complex circuit can use single
voltage source
Resistive divider
• Disadvantage:
I = Vin/Reff = Vout/R2
– dissipates power
Vout =I Vin (R2 / (R1 + R2) )
– easy to overload
Vin
Vout
– need Rload << R2
+
R1
R2
I
New schematic symbol
external connection
Variable voltage divider
• Use potentiometer (= variable resistor)
• Most common: constant output resistance
Variable voltage divider
Vout = Vin (Rout / (Rvar + Rout) )
New schematic symbol:
potentiometer
I
Vin
+
Vout
Rvar
Rout
I
Impedance
Impedance :
• Definition : Impedance is the current resisting and
impeding characteristic of load or conductor in an AC
Circuit.
• Symbol for Impedance: Z
Z = R + jXl - jXc
Where, jXl = Zl and, -jXc = Zc
• Unit for Impedance: Ohms or s.
Revisit Ohm’s Law
Ohms Law:
• Mathematical Statement of the Ohm’s Law:
V = I R for DC circuits
V = I Z for AC Circuits
Note: BOLD letters, in general, represent Vectoral
quantities
“GROUND”
Please float your ideas
Three phase systems
AC-generator
• An AC generator consists of a coil wound on a metallic core
that rotates in a magnetic field.
• The ends of the coil are connected to a pair of slip rings that
are the means to transport the voltage to the external circuit.
Single phase Vs Three phase
• The horsepower rating of three phase motors and the KVA
(kilo-volt-amp) rating of three-phase transformers is about 150%
greater than that for single-phase motors or transformers with a
similar frame size.
Single phase Vs Three phase
• The power delivered by a single-phase system falls to zero three
times during each cycle. Whereas the power delivered by a
three-phase system never falls to zero. The following figure
elaborates it.
Wye or Star connection
• The wye or star connection is made by connecting one end of
each of the three-phase windings together.
• The common point is kept as the ground or reference.
• The voltage measured across a single winding or phase is
known as the phase voltage.
• The voltage measured between the lines is known as line
voltage.
Wye or Star connection
• In a wye connected system, the line voltage is higher than the
phase voltage by a factor of 1.732. Phase current is equal to line
current.
Delta Connection
• In the delta connection, line voltage is equal to the phase
voltage.
• The line current of a delta connection is higher than the phase
current by a factor of 1.732.
Mains circuits
Household electric wiring plan for a flat:
electric
mains supply company’s
cable N main fuse
kW h
meter
consumer unit
mains
switch
L
mains socket
30 A 5 A 15 A 30 A
cable
water heater
air-conditioner
cable
cable
lighting circuit
ring main
cable
2-way switches
mains socket
mains socket
Mains circuits
main supply electric
cable
company’s
main fuse
kilowatt-hour
meter
in parallel
consumer unit (‘fuse box’)
lamps
water
heater airconditioner
All electrical appliances are connected in parallel.
Why?
faults in one circuit will not affect other
circuits.
Mains circuits
mains
supply
cable
electric
company’s
main fuse
kilowatt-hour
meter
consumer unit (‘fuse box’)
lamps
• Each circuit branch has L, N & E wires.
water
heater
airconditioner
• Earth wires are connected to an earthing
electrode buried underground.
consumer unit (‘fuse box’)
It has a main switch:
one can switch off whole circuit
for repair work
or in case of emergency
each circuit is fitted
with a fuse or
circuit breaker
Lighting circuit
5A
• 1 branch for ceiling
lamps: lighting circuit
• Each lamp is controlled by a switch
on wall
• Protected by 5 A fuse
lighting circuit
Two-way switches
The lamp can be switched on at the bottom of the staircase &
then switched off at the top, & vice versa.
Two-way switches
The lamp can be switched on at the bottom of the staircase &
then switched off at the top, & vice versa.
on
off