Topic 5 capacitance in AC circuits topic a5

Solve problems in single and threephase low voltage circuits
Part A
Topic 5: Capacitance in
AC Circuits


Capacitance in AC Circuits


Capacitive Component
–
–

A device that consists of a two metal plates
separated by a dielectric (insulator).
A capacitive component’s function is to store
energy in an electrostatic field.


Capacitance in AC Circuits


Key Characteristic
–

–
–

A capacitive component will ACT TO STORE
ELECTRICAL CHARGE THAT WILL OPPOSE
THE APPLIED VOLTAGE (and therefore current)

It achieves this by storing a negative charge on
one plate and a positive charge on the other.
How strongly it does this is indicated by the
capacitor’s CAPACITANCE, symbol C, measured
in Farads (F)
C


Capacitance in AC Circuits


Effect in an AC circuit
–

–

Since the voltage in an AC circuit is continually
changing (ie alternating between positive voltage
and negative voltage), a capacitor in an AC circuit
continually charges and discharges which then
opposes the change in voltage (and current).
As a result, the capacitor produces a constant
opposition to the flow of alternating current.


Capacitance in AC Circuits


This opposition to alternating current flow is
called CAPACITIVE REACTANCE.

XC =


Where:
–

1
2π ƒ C

Xc is the capacitive reactance in Ohms (Ω)

2π is a constant
– ƒ is the frequency in Hertz (Hz)
– C is the capacitance in Farads (F)
–


Capacitance in AC Circuits


Important!
–

–

CAPACITIVE REACTANCE is an opposition to
current flow like RESISTANCE, but it is NOT the
same as resistance, even though both are
measured in Ohms.
As a result, CAPACITIVE REACTANCE and

RESISTANCE can NOT be simply added to find
the total opposition to current flow in a circuit.


Capacitance in AC Circuits


Key Advantage
–
–

Ability to produce better operation for circuits
containing highly inductive loads.
Ability to limit AC current flow without consuming
any power.


Capacitance in AC Circuits


Examples of Capacitive Components
–
–
–

Capacitor
Capacitor banks (for power factor correction)
Filter or tuning circuits

Capacitance in AC Circuits: Ohm’s
Law
VC

IC

VC

C

IC

XC

VS
ƒ
Simple Capacitive Circuit

Ohm’s Law – capacitive component


Capacitive Reactance: Exercises

C=47µF

C =?
IC=0.723A

IC=?
VS=230V

VS=230V

ƒ=50Hz

ƒ=50Hz

Q1. Determine:

Q2. Determine:

Capacitive reactance XC, and

Capacitive reactance XC, and

Current though capacitor Ic

Capacitance of capacitor C


Capacitive Reactance: Answers




Q1


XC = 67.73Ω



IC = 3.40A

Q2


XC = 318.12Ω



C = 10μF


Capacitive Reactance: Exercises


A 230V, 50Hz AC supply is to be applied to a
ceiling fan circuit using a capacitor speed
control switch. If the current for the ceiling fan
motor needs to be reduced to 0.362 Amps for
the “Low” setting, determine the appropriate
value of capacitance required by for this
setting (assume the motor has no opposition
to current flow).


Capacitive Reactance: Answers


XC = 635.36Ω



C = 5.01μF


Capacitance in AC Circuits:
Capacitance in Series and Parallel

C1

C1

C2

VS
ƒ

C2
IS
VS
ƒ
Capacitive Reactance in Parallel

Capacitive Reactance in Series
X C Total= X C1+X C2+…

1
X C Total

= 1 + 1 +…
X C1 X C2…


Series Capacitive Circuit
VC1

VC2
Kirchoff’s Voltage Law

C1

C2

•The ‘sum’ of the voltage drops in
the circuit will equal the supply
voltage
Vs = VC1 + VC2+…

VS
ƒ

[Purely capacitive circuit only]


Parallel Capacitive Circuit

IC1

IC2
IS

C1

Kirchoff’s Current Law

C2

•The ‘sum’ of the currents
entering a junction will be equal to
the sum of the currents exiting the
junction.

VS

Is = IC1 + IC2+…

ƒ

[Purely capacitive circuit only]


Capacitance in AC Circuits


Exercises on series / parallel combinations


Capacitance in AC Circuits:

Capacitance in Series and Parallel

C1 = 15μF

VS=230V
ƒ=50Hz
Determine the following:
•XC Total
•IS
•VC2

C1 = 220μF

C2=33μF

C2 = 680μF
IS
VS = 32V
ƒ=50Hz
Determine the following:
•XC Total
•IS
•IC1


Capacitance in AC Circuits


Series Answers
–

XC1 = 212.2 Ω

–

XC2 = 96.5 Ω

–

XC Total = 308.7 Ω

–

IS = 0.75A

–

VC2 = 71.9V


Capacitance in AC Circuits


Parallel Answers
–

XC1 = 14.47 Ω

–

XC2 = 4.68 Ω

–

XC Total = 3.54 Ω

–

IS = 9.04 A

–

IC1 = 2.21 A


Review


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

Understand the concept of capacitive reactance;
Understand the application of Ohm’s Law to capacitive
circuits;
Understand and be able to apply Kirchoff’s Voltage law to a

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


Phase Relationship between
Voltage and Current

Resistive Circuit


Phase Relationship between Voltage
and Current: Resistive Circuit

V
R

‘V’ Waveform
‘I’ Waveform
I

I

V

VS
ƒ
Simple Resistive

Circuit

In-phase

Phasor diagram


Phase Relationship between
Voltage and Current

Inductive Circuit


Phase Relationship between Voltage
and Current: Inductive Circuit

‘V’ Waveform
V
‘I’ Waveform
I

L

V

VS
ƒ
Simple Inductive Circuit

I

Out-of-phase LAG by
900E

Phasor diagram