Topic 3 resistance in AC circuits topic a3

Solve problems in single and threephase low voltage circuits
Part A
Topic 3: Resistance in
AC Circuits


Resistance in AC Circuits


Resistive Component
–

–



Any device that consists of a ‘conductor’ with an atomic
structure that does not allow electrons to move as easily as
a normal conductor.
A resistive component’s function is to convert electrical
energy into heat energy.

Key Characteristic
–
–

A resistive component will OPPOSE THE FLOW OF
CURRENT.
It achieves this by slowing the flow of electrons by not
allowing them to cascade through as quickly.

Resistance in AC Circuits


Symbol ~ R



Unit of measurement ~ OHMS (Ω)


Resistance in AC Circuits


In a purely resistive AC circuit, the circuit can
be analysed using the same principles as DC
circuits.
–
–
–
–
–

Ohm’s Law
Resistors in Series
Resistors in Parallel
Kirchoff’s Voltage Law
Kirchoff’s Current Law

Resistance in AC Circuits: Ohm’s Law
VR

R

VR

IR

IR

R

VS
ƒ
Simple Resistive Circuit

Ohm’s Law – Resistive component


Resistance in AC Circuits: Resistance
in Series and Parallel
R1

R1

R2

R2
VS

ƒ

IS
VS
ƒ
Resistance in Parallel

Resistance in Series
RTotal= R1+R2+…

1

= 1 + 1 +…

RTotal R1 R2…


Kirchoff’s Voltage Law: Series
Resistive Circuit
VR1

VR2

R1

R2

Kirchoff’s Voltage Law
•The ‘sum’ of the voltage drops in
the circuit will equal the supply

voltage

VS

Vs = VR1 + VR2+…

ƒ

[Purely resistive circuit only]


Parallel Resistive Circuit

IR1

R1
Kirchoff’s Current Law
R2

IR2
IS
VS
ƒ

•The ‘sum’ of the currents
entering a junction will be equal to
the sum of the currents exiting the
junction.
Is = IR1 + IR2+…
[Purely resistive circuit only]

Power in a Resistive Circuit



Since a resistor converts electrical energy
into heat, then POWER is dissipated.
This can be calculated by:

P = VI
Or

P = I2R
Or

P = V2/R


Resistance In AC Circuits: Exercises
Question 1:
R1

R2

50Ω

80Ω

IR3

IS
VS=230V
ƒ=50Hz

R3
100Ω

Determine:
•RTotal
•IS
•VR2
•IR3
•PR2


Resistance In AC Circuits: Exercises


Answers


RTotal = 94.4Ω



IS = 2.44A



VR2 = 108V



IR3 = 1.08A



PR2 = 146W


Resistance In AC Circuits: Exercises
Question 2:
R1

IR2

5Ω

R2
?Ω

IR3
IS=4A
VS=50V
ƒ=50Hz

Determine:
•IR2

R3

•R2

20Ω

•PR1


Resistance In AC Circuits: Exercises


Answers


IR2 = 2.5A



R2 = 12Ω



PR1 = 80W


Resistance In AC Circuits: Exercises
Question 3:
R2

IR2

R4

?Ω

5Ω

IR3=1.5A
R1

IS

•VS
IR4=2A

R3
10Ω

Determine:

25Ω
VS=? V
ƒ=50Hz

•IS
•R2


Resistance In AC Circuits: Exercises


Answers


VS = 25V



IS = 3A



R2 = 30Ω


Review


At this stage, you should have a clear understanding
of resistance in AC circuits, including:
–
–
–
–
–

Understand the concept of resistance in AC circuits;
Understand the application of Ohm’s Law;
Understand and be able to apply Kirchoff’s Voltage law to a
purely resistive circuit;

Understand and be able to apply Kirchoff’s current Law to a
purely resistive circuit;
How to make calculations involving V, I, R, and P in
combined series/parallel circuits.