TOPIC 2- sinusoidal steady state

DET20033-ELECTRICAL
CIRCUITS
TOPIC 2:

SINUSOIDAL STEADY-STATE
CIRCUIT ANALYSIS

Reference : CHAPTER 15/16
Electrical and Electronic Principles and Technology

Third edition
John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,

FIIE, FIMA, FCollT

COURSE LEARNING

OUTCOMES

• Study the AC basic circuits [CLO1]
• Understand the circuit with inductive

and capacitive load [CLO1]
• Understand the series/parallel R-L-C

circuits [CLO1]
• Understand the combination of series-

parallel R-L-C circuits [CLO1]
• Understand the concept of work,

power and energy [CLO1]
• Understand the power consumption in

AC circuits [CLO1]

At the end of the lesson students
should be able to:

• 3.2 Understand the circuit with inductive and
capacitive load
3.2.1 Calculate the current and voltage in R-
L, R-C and R-L-C:
a. Series circuits
b. Parallel circuits

3.2.2 Construct the vector diagram to show:
a. Current is taken as reference in series
circuit
b. Voltage is taken as reference in parallel
circuit

Single-phase SERIES a.c.circuits

Reference : CHAPTER 15

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

PURELY RESISTIVE AC CIRCUIT

REACTANCE R=V/I (Unit in Ω)

VR = VM sin wt

IR = IM sin wt

VR are in-phase with IR. Phase angle equal to 0°

PURELY INDUCTIVE AC CIRCUIT

REACTANCE XL=VL/IL @ XL=2πfL (Unit in Ω)

VL = VM sin (wt +90°)
IL = IM sin wt

IL lags VL by 90° or VL leads IL by 90°

PURELY CAPACITIVE AC
CIRCUIT

Ic leadsVc by 90◦

REACTANCE XC=VC/IC @ XC=1/2πfC (Unit in Ω)

Vc = VM sin (wt - 90°)
Ic = IM sin wt

Vc lags Ic by 90° or Ic leads Vc by 90°

Relationship Between R/XL/XC
and Frequency

❑Inductance reactance XL increase as the frequency across it
increase. Directly proportional.
❑Capacitive reactance Xc of the capacitor decrease as the
frequency across it increases. Inversely proportional
❑Resistance does not change with frequency. R remains
constant even if the frequency is increase or decrease.

LAGS

C IVI L

LEADS

For Capacitor, I lead V by 90° or V lags I by 90°
For Inductor, V lead I by 90° or I lags V by 90°

Problem 1. Exercise

(a) Calculate the reactance of a coil of inductance 0.32H when it is connected

to a 50 Hz supply. (100.5 Ω)

(b) A coil has a reactance of 124Ω in a circuit with a supply of frequency 5 kHz.

Determine the inductance of the coil. (3.95mH)

Problem 2.
Determine the capacitive reactance of a capacitor of 10 μF when connected to

a circuit of frequency (a) 50 Hz (318.3 Ω) (b) 20 kHz (0.796 Ω)

Problem 3.
Calculate the current taken by a 23 µf capacitor when connected to a 240V,

50Hz supply. (1.73A)

Single-phase SERIES a.c.circuits

Reference : CHAPTER 16

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

RL SERIES AC CIRCUIT

RL SERIES AC CIRCUIT

❑ In series circuit, current is taken as reference because current is the same
in series circuit.

❑ Total current IT in RL circuit always lags the source voltage VS
❑ Resistor voltage VR is always in phase with the current
❑ In an ideal inductor, the voltage VL always leads the current by 90°
❑ Total Impedance Z = R + jXL or :

❑ Total voltage = Z = VR + jVL or :

EXERCISE

Problem 1.
A coil has a resistance of 4 and an inductance of
9.55 mH connected to a 240V, 50 Hz supply.

Calculate
(a) the reactance (XL=3Ω)
(b) the impedance (Z=5Ω)
(c) the current taken from (I=48A)

Determine also the phase angle between the
supply voltage and current. (36.87◦ lagging).
Draw the phasor diagram

Problem 2. EXERCISE

A coil consists of a resistance of 100 and an

inductance of 200 mH. If an alternating voltage, v,

given by v=200 sin 500t volts is applied across the

coil, calculate
(a) The circuit impedance (Z=141.4Ω)

(b) The current flowing (I=1.41A)

(c) The p.d. across the resistance (Vr=141V)

(d) The p.d. across the inductance (Vl=141V)

(e) The phase angle between voltage and current.
(φ=45◦ or π/4 rads)

(f) Draw the phasor diagram for voltages.

RC SERIES AC CIRCUIT

RC SERIES AC CIRCUIT

❑ In series circuit, current is taken as reference because current is the same
in series circuit.

❑ Total current IT in RC circuit always leads the source voltage VS
❑ Resistor voltage VR is always in phase with the current
❑ In an ideal capacitor, the voltage VL always lags the current by 90°
❑ Total Impedance Z = R - jXc or :

❑ Total voltage = V= VR - jVL or :

Problem 1. EXERCISE

A capacitor C is connected in series with a 40ohm resistor

across a supply of frequency 60 Hz. A current of 3A flows
and the circuit impedance is 50 Ω.

Calculate
(a) the value of capacitance, C, (88.42 μF)
(b) the supply voltage, (150V)
(c) the phase angle between the supply voltage and

current, (36.87◦ leading.)
(d) the p.d. across the resistor (120V)
(e) the p.d. across the capacitor. (90V)
(e) Draw the phasor diagram



R-L-C SERIES AC CIRCUIT

PHASOR DIAGRAM

CIRCUIT DIAGRAM

XL > XC (inductive) XC > XL (capacitive

VOLTAGE TRIANGLE VOLTAGE TRIANGLE

EXERCISE

Problem 1.
A coil of resistance 5 and inductance 120mH in
series with a 100 uf capacitor, is connected to a
300V, 50 Hz supply.
Calculate

(a) the current flowing, (38.91A)
(b) the phase difference between the supply voltage

and current, (49.58◦)
(c) the voltage across the coil (1480V)
(d) the voltage across the capacitor (1239V)

(e) Draw the phasor diagram

Try to solve PROBLEM 16 in CHAPTER 14!!!

Solution





Single-phase PARALLEL a.c.circuits

Reference : CHAPTER 16

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

by
TS ZULKIFLI & TS SHALIZAN /JKE/PKK/2018

RL PARALLEL AC CIRCUIT

❑ In parallel circuit,
voltage is taken as
reference because
voltage is the same in
parallel circuit.

FORMULA :

Problem 1. EXERCISE

A 20Ω resistor is connected in parallel with

an inductance of 2.387mH across a 60V,

1 kHz supply. Calculate

(a) the current in each branch, (IR=3A, IL=4A)

(b) the supply current, (I=5A)

(c) the circuit phase angle, (θ=53.13° LAGGING)

(d) the circuit impedance, (Z=12Ω)

(e) the power consumed. (P=180W)

(f) Draw the phasor diagram

DO EXERCISE 90 ON CHAPTER 16 !

Solution



RC PARALLEL AC CIRCUIT

FORMULA :

EXERCISE

Problem 1.
A 30μF capacitor is connected in parallel with an
80Ω resistor across a 240V, 50 Hz supply.
Calculate
(a) the current in each branch, (IR=3A, IC=2.262A)
(b) the supply current, (I=3.757A)
(c) the circuit phase angle, (θ=37.02° LEADING)
(d) the circuit impedance, (Z=63.88Ω)
(e) the power dissipated,(P=720W)
(f) the apparent power,(S=901.7VA)

DO EXERCISE 91 ON CHAPTER 16 !





L-C PARALLEL AC CIRCUIT

Problem 1. EXERCISE

A pure inductance of 120mH is connected in
parallel with a 25 μF capacitor and the network is

connected to a 100V, 50 Hz supply. Determine

(a) the branch currents, (IL=2.653A, IC=0.786A)

(b) the supply current (I=1.867A)

(c) its phase angle, (θ=90° LAGGING)

(d) the circuit impedance, (Z=53.56Ω)

(e) the power consumed. (P=0W)

DO EXERCISE 92 ON CHAPTER 16 !

R-L-C PARALLEL AC CIRCUIT

It
Ic IL Ir

EXERCISE

Problem 1.

Given L=120mH parallel with C=25µ, V=100V,

50 Hz supply. Determine:

(a) the branch currents, (IL=2.65A, IC=0.755A)

(b) the supply current, (I=1.864A)
(c) the circuit impedance, (Z=53.64Ω)

(D) the power dissipated,(P=0W)

EXERCISE

Problem 2.

Find Z and the phase angle for the circuit:

80Ω 100Ω 100Ω

(Z=70.7Ω, θ=45°)

EXERCISE

Problem 3.

Find I and the phase angle for the circuit. (I=2.32A, θ=12.42°)
Find Z. (Z=2.15Ω)

5<0°v 5Ω 10Ω 2.2Ω

EXERCISE

Problem 4.

Find i. Current branch. (Ir=3.5A, IL = 15.3 A, Ic = 0.43A)

ii.Draw phasor diagram for circuit
iii. Find Impedance Z

115V 20mH 33Ω
60Hz
10uF

Single-phase SERIES/PARALLEL
a.c.circuits

Reference : CHAPTER 15/16

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

by
TS ZULKIFLI & TS SHALIZAN /JKE/PKK/2018

EXERCISE

Problem 1.
A coil of inductance 159.2mH and R=40Ω is connected in
parallel with a 30µF capacitance across 240V, 50Hz supply.
Calculate :
(a) I in the coil and phase angle, (IRL=3.75<-51°A)
(b) I in the capacitor and phase angle (IC=2.26<90°A)
(c) the circuit impedance, (Z=98.5<16°Ω)
(d) the supply current and phase angle, (I=2.44<16°A)
(e) the power consumed. (P=562.9W)
(f) the apparent power (S=585.6VA)
(g) the reactive power (Q=161.4VAR)

EXERCISE

Problem 2.
A coil of inductance 318.4mH and R=60Ω is

connected in parallel with a 15uF capacitance

across 200V, 50Hz supply.

Calculate :
(a) I in the coil and phase angle, (IRL=1.71<-59°A)

(b) I in the capacitor and phase angle

(IC=0.94<90°A)

(c) the circuit impedance, (Z=192<31°Ω)

(d) the supply current and phase angle, (I=1<-31°A)

(e) the power consumed. (P=171.4W)

Problem 3. EXERCISE

10<0°
5kHz

Find:
(a) Z total (Z=11.4k<56.5°Ω)
(b) I total (Z=885u<-56.5°A)
(c) θ (56.5°Ω)

EXERCISE

Problem 4. (TUTORIAL 3 : Soalan 1)

10<0°

Find Ztotal and Itotal
Sketch phasor diagram for voltages and currents

EXERCISE

Problem 5. (TUTORIAL 3 : Soalan 2)

10<0°
Find Ztotal and Itotal

TUTORIAL 3

** Please submit Tutorial 3 on

…………..

POWER IN AC CIRCUIT

Reference : CHAPTER 15

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

by
ISMA_SHAMSURIA/JKE/2011

Power in pure resistance, inductance
and capacitance