CHAPTER 2

Purely Capacitance
Purely capacitance is an ac circuit containing only a
capacitor.

Purely Capacitance Circuit

Purely Capacitance

Purely capacitance (a) Waveform (b) Vector Diagram

In purely capacitance circuit, the current leads the
voltage by a phase angle of 90 degree .

Purely Capacitance

The effects of capacitance in AC circuit are:

a) Capacitance reactance value is equal to the
resistance value of resistor.

b) The capacitance reactance is directly
proportional to the frequency. When
frequency is increases, hence capacitance
reactance is also increases.

Resistance (R) and reactance ( XL or Xc) are different
althougth same in unit (Ω).

Resistance is oppose to the current flow in both DCandAC
circuits.

Reactance is oppose to the current flow only in ACcircuit

Impedance (Z) also oppose to the current flow in only AC
circuit.

2.6 ComputeseriesR-L,R-Cand R-L-C
circuits (ACcircuitAnalysis)

Series RLCircuit SeriesResistance and Inductance (RL)

• The RLcircuit is the combination
between resistor and inductor
in series. In a series circuit, the
current value is the same for
each load.

• Thus,the current (I) become the
reference factor in the vector
diagram.

2.6 ComputeseriesR-L,R-Cand R-L-C
circuits (ACcircuitAnalysis)

Vector Diagram for Series RLCircuit
• Thevalue of the current islimited by resistance and inductance

reactance.
• Thecurrent flows through the resistance, Ris in phase with the voltage but lags

behind the voltage by a phase angle of 90degree when flows through the
inductance reactance, XL.

Based on Figure “Vector Diagram for Series RLCircuit” ,
the magnitude of the supply voltage (V) can determine
using Pythagoras theorem

The voltage drop at each components can be calculate
using equations;

• Theimpedance is the amount of impediment/resistance that exist in
the ac circuit. Thesymbol for impedance is Zand unit is Ohm(Ω).

• An impedance triangle in Figure “Impedance Triangle for RL” showthe
relationship between the resistance (R),inductance reactance (XL)and
impedance (Z) can be generated based on the “Vector Diagram for
Series RLCircuitFigure”.

Impedance can be calculates using Equation below;

or

Phaseangle and power factor for RL circuit can be calculates
using equations below:

QUICK EXERCISE

TheRLseries circuit have 10Ω resistor, 0.2H inductor
and supplied with 250v 50Hz ACsupply.
Calculates;

i. lmpedance, Z
ii. Current, I
iii. Phaseangle, θ

SeriesResistance and Capacitance (RC)

Series RC Circuit

• TheRCcircuit is the combination between resistor and capacitors in
series.

• Thecurrent value is the samefor each load. Thus, the current (I)
become the reference factor in the vector diagram

SeriesResistance and Capacitance (RC)

Vector Diagram for Series RCCircuit

• Thevalue of the current is limited by resistance, Rand capacitance
reactance, XC.

• Thecurrent flows through Ris in phase with the voltage but leading by a
phase angle of 90degree when flows through inductance reactance.

• Figure below is a vector diagram for series RCcircuit.

Based on Figure “Vector Diagram for Series RCcircuit” ,
the magnitude of the supply voltage (V) can determine
using Pythagoras theorem

Impedance Triangle

• An impedance triangle in Figure “Impedance Triangle for RC”
shows the relationship between the resistance (R), capacitance
reactance (Xc) and impedance (Z) can be generated based on the
“Vector Diagram for Series RC Circuit ”.
Impedancecanbe calculates using Equation below :

OR

Where XC= 1 / (2ΠfC)

Phase angle and power factor for RC circuit can be
calculates using equations below:

QUICK EXERCISE

A10Ω resistor and 200µF capasitor are
connected in series across a 120V, 50V ACsupply.
Calculate:

i. Impedance, Z
ii. Current, I
iii. Power factor, pf

Series Resistance, Inductance and
Capacitance (RLC)

• The RLCcircuit is the combination of resistor, indictor and
capacitor in series with AC supply.

• The current value is the same for each load. Thus,the
current (I) become the reference factor in the vector
diagram.

Series RLC Circuit

In RLCthere are (2) conditions should to be
consider;

a) inductance reactance is greater than capacitance
reactance, XL >XC

Theimpedance for RLC can be
calculate using Equation below;

(a)Vector Diagram (b) Impedance Triangle for XL> XC

Voltages drop at each components can be calculate using equations below;

Phaseangle and power factor for RCcircuit can be calculates
using equationsbelow:

POWER FACTOR

• Powerfactor can be express in the form of percentage (%) or fractional
numbers.

• It is known as cosθ and referred to as leading (lead) or lagging
(lag) in which the phase angle between voltage and current.

Power factor is a ratio between real power and apparent power.

Power factor isa ratio between resistance and impedance.

Leading power factor is voltage leading the current when
voltage as reference factor and value of the voltage is
positive.

Lagging power factor is voltage lagging the current the
when voltage as reference factor and value of the
voltage is negative.

Best value of power factor is where Cos θ = 1 or nearly 1.

POWER IN AC CIRCUIT

There are 3 types of power in the ac circuit;

Apparent power, S

• Power is reduced due to the existence of the reactance that
cause current and voltage is not in phase.

• The separation of current and voltage caused the power in
the circuit will be reduced.

• The symbol is Sand unit is Volt – Ampere (VA)

Apparent Power = Voltage x Current

POWER IN AC CIRCUIT

Real Power, P

• Real power or active power is the power
consumed or absorbed by the resistor
components in ac circuits.

• The symbol is P and the unit is watt (w).

Real Power = Voltage x Current x Power Factor

POWER IN AC CIRCUIT

Power triangle shows the relationship between the
apparent power, real power and the reactive power.

Power Triangle

QUICK EXERCISE

ARLCcircuit wasconnected in series with 100 ohms
resistor, 200mikroF capacitor and 100mH inductor
then supplied with ACpower supply 240V, 50Hz.

Calculate;

i. lmpedance, Z
ii. Current, I
iii. Power factor and phase angle
iv. Power in kVA, kW and kVAR.

POWER IN AC CIRCUIT

Real Power, P

• Real power or active power is the power
consumed or absorbed by the resistor
components in ac circuits.

• The symbol is P and the unit is watt (w).

Real Power = Voltage x Current x Power Factor

2.7 BASIC PRINCIPLE OF AC SYSTEM (3Φ &1Φ)

THREE PHASE SYSTEM(3Φ )

i. Three-phase systemisa commonmethod of alternating
current electric power generation, transmission, and
distribution.

ii. It is a type of poly phase systemwhich hastwo or more voltage source
with fixed phase angle difference.

iii. Three phase systemis a systemthat hasthree source voltage of the
samemagnitude produced by the three separate coil conductor which
space 120degree apart as shownin Figure shown.

iv. Normally a three phase supply has three (3) live wire or phase
conductor of Red phase (R), Yellow phase (Y) and Blue phase(B).

2.7 BASIC PRINCIPLE OF AC SYSTEM (3Φ &1Φ)

THREE PHASE SYSTEM(3Φ )

RR”coil, Emsin0 = zero,
YY” coil, Em sin120degree = 0.866Em volt and BB”coil ,
Emsin240degree equal = -0.866 Emvolt.

DIFFERENT BETWEENSINGLE PHASE & THREE
PHASE SYSTEM

Three phase system basically used in starting the 3phase
machines, supply power to large factories and for transmission
and distribution 3 phase voltage. The advantages of 3 phase
over single phase systems are:

i. More economical due to less construction and maintenance costs.The
conductor used is smaller, thusthe needs of copper can be reduced

ii. Easy to install due to smaller and lighter cable used. Therefore the
smaller structures supporters can be used and the distance between the
supporters can be relatively long.

iii. Thecharacteristics of 3phase equipment have a better operating
starting due to its stable and fixed power.

iv. Electrical energy supplied is higher than single phase.

Three phase system basically used in starting the 3phase
machines, supply power to large factories and for transmission
and distribution 3 phase voltage. The advantages of 3 phase
over single phase systems are:

v. Most large motors used for induction motor 3phase can stand alone
without the additional equipment suchas capacitors, centrifugal
switches or other additional circuits

vi. The output Production and equipment quality of work for 3phase
system is better than single phase because of the higher efficiency and
power factor.

END OF TOPIC 2,
Summary-Q&A session