ac principles series rlc

8/2/2019 AC Principles Series RLC

http://slidepdf.com/reader/full/ac-principles-series-rlc 1/89



The same applies to AC circuits

Current is the same in all components V supply will be the sum of VR and VXL

The total opposition to current flow, impedance in a.c.circuits, is the sum of R and XL



If I = 2A, R = 40, XL = 30 Then:



The supply voltage would be?

100V



WHY?????

How can 80 + 60 = 100

It must be remembered that the voltage

drop across the resistor is in phase withcurrent and the voltage drop across the

inductor leads the current by 90°

The problem must be solved as a vector or

phasor



As this is a series circuit current is

common to all components and is

used as reference.



The voltage drop across the

resistor is in phase with the current



The voltage on the inductor leads

by 90°



Using the end to end method VXL

can be drawn at the end of VR



The supply voltage can now be

found



The angle between the voltage and

the current is also useful



For our circuit



Therefore



Total opposition to current flow

Rather thanresistance, this isreferred to as

impedance on a.c.circuits

It is still measured inohms, but has thesymbol Z

For our circuitcalculate theimpedance



Using Ohm¶s law

Z =V SUPPLY

I SUPPLY

Z =100

2

Z = 50



It is possible to make another

triangle, known as an impedance

triangle



Our impedance triangle is shown

as:



The power consumed by the circuit

can now be determined



The inductor consumes no power



The inductor appears to consume 120W, but

watts cannot be used. So VA, Volts x Amps,

is used. VAR for reactive



The circuit consumes 160W but

appears to consume 200.



Power triangle



This can be shown as:



Power factor

Power factor is the ratio between true Power and

Apparent Power.

This is also the cosine of the angle between the

True and Apparent power



Using the triangles

Using Ohm¶s law (V = IR) and the power formula

(P = VI) you can move from one triangle to the

other.

Multiple by current to move to the right

Divide by current to move to the left



Multiply or divide a side by current

to move between triangles



Resistors and Capacitors on AC

Current is the same in all components V supply will be the sum of VR and VXC

The total opposition to current flow, impedance in a.c.circuits, is the sum of R and XC



If I = 2A, R = 40, XC = 30 Then:




100V



WHY?????

How can 80 + 60 = 100


drop across the resistor is in phase withcurrent and the voltage drop across the

Capacitor lags the current by 90°

The problem must be solved as a vector or

phasor





used as reference.



The voltage on the capacitor lags

by 90°



Using the end to end method VXC

can be drawn at the end of VR



The supply voltage can now be

found



The angle between the voltage and

the current is also useful



For our circuit



Therefore




Rather thanresistance, this isreferred to asimpedance on a.c.circuits

It is still measured inohms, but has thesymbol Z

For our circuitcalculate theimpedance



Using Ohm¶s law

Z =V SUPPLY

I SUPPLY

Z =100

2

Z = 50

It i ibl t k th





triangle




as:



The inductor consumes no power



The inductor appears to consume 120W, but

watts cannot be used. So VA, Volts x Amps,

is used. VAR for reactive



Power factor


Apparent Power.





Summary

All three triangles are the same shape, the difference is the size, each triangle is 2

times larger/smaller than the other. Which is the value of the current



Using the triangles



other.

Multiple by current to move to the right Divide by current to move to the left



Series Resistor, Inductor and

Capacitor

Current is the same in all components

V supply will be the sum of VR,VXL and VXC

The total opposition to current flow, impedance in a.c. circuits, is the sumof R, XL and XC



If I = 2A, R = 40, XL= 45, XC = 15 Then:



Once again we need to solve via

phasor


drop across the resistor is in phase with

current

The voltage drop across the Inductor leads

the current by 90°

The voltage drop across the Capacitor

lags the current by 90°






used as reference.



The voltage across the inductor

leads by 90°



The voltage across the Capacitor

lags by 90°

VXL and VXC are 180° out of phase



VXL and VXC are 180 out of phase

with each other, and therefore one

can be subtracted from the other



Supply voltage is the phasor sum

of VR and (VXL ± VXC)



Using Ohm¶s law

Z =V SUPPLY

I SUPPLY

Z =100

2

Z = 50






triangle

O i d t i l i h




as:

Th d b th i it





Th i d t d it



The inductor and capacitor

consumes no power

The inductor and capacitor appear to



The inductor and capacitor appear to

consume power but do not. So VA, Volts x

Amps, is used. VAR for reactive

Th i it 160W b t



Power triangle



Power factor


Apparent Power.





Summary

All three triangles are the same shape, the difference is the size, each triangle is 2times larger/smaller than the other. Which is the value of the current



Using the triangles



other.

Multiple by current to move to the right Divide by current to move to the left




What if XC is greater than XL?

If XC is larger than XL

then the triangle will

simply be upside down

If using Pythagoras

theorem, a negativenumber squared equals a

positive number (some

modern calculators do not

do this, so check your calculator now)



Using the internet

On many sites XL and XC have a j in front

of them to indicate vertical component of

triangle.

XC is also given a negative value ± jXC

This makes Kirchhoff's laws more

accurate, ie VS it the sum of VR, VXL and

VXC.

At trade level however we say VXL - VXC

ac principles series rlc

Documents