Alternating-Current Circuits

Physics 1112

Alternating current is commonly used everyday in homes and businesses throughout the word to power various electrical appliances

max sin

22

v V t

fT

The voltage supplied by an AC source is sinusoidal with a period T

Voltage in AC Circuits

maxm

maxm

0

sin I sin

I

R

R ax

ax

v i R

Vvi t t

R RV

R

Resistors in AC Circuits

RMS Current & RMS Voltage• Average value of current is referred as RMS Current & average value of voltage is referred as RMS Voltage

• The notation rms stands for root-mean-square, which means the square root of the mean (average) value

2

2 2max

mm

2

mm

( )

1

2I

0.707 I2

0.7072

rms avg

axrms ax

avg rms

axrms ax

I i

i I

I

P I R

VV V

Inductors in an AC Circuit

Instantaneous current and voltage are out of phase by /2

maxmI ax

V

L

L is defined as inductive reactance XL

LX L

Capacitors in an AC Circuit

Instantaneous current and voltage are out of phase by /2

maxm maxI

(1/ )ax

VC V

C

(1/C) is defined as capacitive reactance XC

1/CX C

The RLC Series Circuit

m

m

m

I sin sin

I sin( ) cos2

I sin( ) cos2

R ax R

L ax L L

C ax C c

v R t V t

v X t V t

v X t V t

2 2 2 2max m m m

2 2max m

maxm 2 2

maxm

( ) (I ) (I I )

I ( )

I( )

I

R L C ax ax L ax C

ax L C

ax

L C

ax

V V V V R X X

V R X X

V

R X X

V

Z

Z is called impendence of circuit

Resonance in a Series RLC Circuit

2 2( )

rmsrms

rmsrms

L C

VI

ZV

IR X X

The angular frequency at which XL-XC=0 is called the resonance frequency of the circuit

0 0

0

0

1/

1

L C

L C

X X

X X

L C

LC