basic ac circuits

Chapter 4R-L-C A.C. CIRCUIT

SERIES RESONANCEA.C. POWER TRIANGLE

POWER FACTOR CORRECTION

R-L-C AC CIRCUIT

Pure Resistive AC Circuit

Pure Capacitive AC Circuit

Pure Inductive AC Circuit

Circuit

PhasorDiagram

I-VWaveform

current IR and applied voltage VR are in phase

current IL lagging theapplied voltage VL by 90◦

current IC leading the applied voltage VC by 90◦

Reactance R

in a capacitor (C) the current (I) leads voltage (V), and voltage (V) leads

current (I) in an inductor (L).

C-I-V-I-L

Impedance, Z = Opposition for current to change (or to flow) in circuit due to capacitance (capacitive reactance, XC) AND inductance (inductive reactance, XL) (unit=ohm, Ω)

Reactance, X = Opposition to a change in current (or to flow) due to capacitance (capacitive reactance, XC) OR inductance (inductive reactance, XL)

Terms

Example1 2

Exercise1

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RC Series Circuit

Phasor Diagram

Example1 2

Exercise1

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1234

567

R-L-C Series Circuit

Z

@

Capacitive CircuitInductive Circuit

Resonance

Example1

Example

Exercise1

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SERIES RESONANCE

Properties

Phasor Diagram

Resonance

Properties

7 Things you need to know about RLC Series Circuits.

1. AT RESONANCE (ƒr) XC is equal to XL (but in anti-phase)2. AT RESONANCE (ƒr) VC is equal to VL (but in anti-phase)3. AT RESONANCE (ƒr) Impedance (Z) is at minimum and equal to the

RESISTANCE (R)4. AT RESONANCE (ƒr) Circuit current is at a maximum.5. AT RESONANCE (ƒr) The circuit is entirely resistive.6. BELOW RESONANCE (ƒr) The circuit is capacitive.7. ABOVE RESONANCE (ƒr) The circuit is inductive.

Q-FactorResonance

Example1 2

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BandwidthResonance

Bandwidth

Example

POWER TRIANGLE

D.C. POWER TRIANGLE

A.C. POWER TRIANGLE

(a) For a purely resistive a.c. circuit, the average power dissipated, P, is given by: P=VI=I2R= V2/R watts (V and I being r.m.s. values) See Fig.(a)

(b) For a purely inductive a.c. circuit, the average power is zero. See Fig.(b)

(c) For a purely capacitive a.c. circuit, the average power is zero. See Fig.(c)

A.C. POWER TRIANGLE

Example1

Exercise1

𝑉 𝑟𝑚𝑠=𝑉𝑀𝑎𝑥

√2

𝐼 𝑟𝑚𝑠=𝐼𝑀𝑎𝑥

√2

𝑉=𝑉𝑚𝑎𝑥𝑆𝑖𝑛𝜔𝑡𝐼=𝐼𝑚𝑎𝑥𝑆𝑖𝑛𝜔𝑡

Power Triangle

Apparent power (VA)

Real power (Watt)

Reactive power (VAR)

Power Triangle Analogy

Apparent power (VA)

Real power (Watt)

Reactive power (VAR)

Example1

Exercise1

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POWER FACTOR CORRECTION

Low Power Factor

High Power Factor

REAL

‘TEH

’RE

AL P

OW

ER

REAL

‘TEH

’RE

AL P

OW

ER

‘WASTED” Reactive‘WASTED” Reactive

Power Factor Correction

• In any a.c. circuit, power factor = cos θ, where θ is the phase angle between supply current and supply voltage.

Power Factor Correction

• Industrial loads such as a.c. motors are essentially inductive (i.e. R-L) and may have a low power factor.

• For example, let a motor take a current of 50A at a power factor of 0.6 lagging from a 240V, 50Hz supply, as shown below.

?

How can this power factor of 0.6 be ‘improved’ or ‘corrected’ to, say, unity?

Power Factor Correction• Unity power factor means: cos θ = 1

from which, θ = 0• How can the circuit being modified and that circuit phase

angle is changed from 53.13◦ to 0◦?• The answer is to connect a capacitor in parallel with the

motor as shown belowWhen a capacitor is connected in parallel with the inductive load, it takes a current shown as IC . In the phasor diagram, the current IC is shown leading the voltage V by 90◦

The supply current is shown as I and is now the phasor sum of IM and IC.

Power Factor Correction

• In the phasor diagram, current I is shown as the phasor sum of IM and IC and is in phase with V , i.e. the circuit phase angle is 0◦, which means that the power factor is cos 0◦ = 1.

• Thus, by connecting a capacitor in parallel with the motor, the power factor has been improved from 0.6 lagging to unity.

53.13O

IM

IS

ISa

b

Power Factor Correction• Before the capacitor was connected, the supply current was

50A. Now it is 30A.• In conclusion, the advantage of power factor improvement –

the supply current has been reduced.• When power factor is improved, the supply current is

reduced, the supply system has lower losses (i.e. lower I2R losses) and therefore cheaper running costs.

Example1

Power Factor Correction

• In practical situations a power factor of 1 is not normally required but a power factor in the region of 0.8 or better is usually aimed for. (Actually, a power factor of 1 means resonance!)

Example2

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Thank You