LECTURE 24

Pick up • lecture notes

Pick up • lecture notes

Average and root-mean-square

T

av tdtIT

I0

)(1T

av tdtIT

I0

)(1

2

2/1

0

2 )(1

avrms

T

rms

II

tdtIT

I

2

2/1

0

2 )(1

avrms

T

rms

II

tdtIT

I

Exercise 1: The average of the voltage signal shown is(a) Vo(b) 0(c) Vo/2

The rms of the voltage signal shown isa.) Vo b.) 0 c.) Vo/2 d.)

Exercise 1: The average of the voltage signal shown is(a) Vo(b) 0(c) Vo/2

The rms of the voltage signal shown isa.) Vo b.) 0 c.) Vo/2 d.) 2/0V

Exercise 2: The voltage signal is rectified” by eliminating negative voltages. The rms for the rectified signal is (a) 0(b) Vo(c) Vo/2(d)

The average for the rectified signal is a) 0 b.) Vo c.) Vo/2 d.)

Exercise 2: The voltage signal is rectified” by eliminating negative voltages. The rms for the rectified signal is (a) 0(b) Vo(c) Vo/2(d)

The average for the rectified signal is a) 0 b.) Vo c.) Vo/2 d.)

20V

Rectified

20V

Resistor in AC circuit

RtItE )()( RtItE )()(

Kirchhoff’s law

RtItE

tEtE

)()sin(

)sin()(

0

0

)sin()( 0 tR

EtI

Current in phase with voltageCurrent in phase with voltage

Concept Test: As the frequency of the generator is increased, the average power dissipated in the resistor A) increases. B) does not change. C) may increase or decrease depending on the magnitude of the original frequency.

Concept Test: As the frequency of the generator is increased, the average power dissipated in the resistor A) increases. B) does not change. C) may increase or decrease depending on the magnitude of the original frequency.

Inductor in AC circuit

)sin()cos()(

)()()(

)cos()(

00

0

tL

Et

L

EtI

dt

tdILtVtE

tEtE

L

)2/cos()( 0 tItI

Voltage leads the current by 90 degreesVoltage leads the current by 90 degrees

LX L XL: inductivereactance

Effectiveresistance

Concept Test: As the frequency of the generator is doubled, the maximum current through the inductor

A) increases by a factor of 2. B) does not change. C) decreases by a factor of 2. D) increases by a factor of 4. E) decreases by a factor of 4.

Concept Test: As the frequency of the generator is doubled, the maximum current through the inductor

A) increases by a factor of 2. B) does not change. C) decreases by a factor of 2. D) increases by a factor of 4. E) decreases by a factor of 4.

Capacitor in ac circuits

)sin()(

)(

)()()(

)cos()( 0

tCdt

tdQtI

C

tQtVtE

tEtE

C

)2/cos()/(1

)( 0

tC

EtI )2/cos(

)/(1)( 0

t

C

EtI

CXC

1 Capacitative reactance

Voltage lags the current by 90 degreesVoltage lags the current by 90 degrees

Concept Test: The loudspeaker shown belowreceives from the amplifier both high and lowfrequency signals. Which speaker emits the high frequency signals:

A) speaker 1B) speaker 2C) both speakersD) need more information.

Concept Test: The loudspeaker shown belowreceives from the amplifier both high and lowfrequency signals. Which speaker emits the high frequency signals:

A) speaker 1B) speaker 2C) both speakersD) need more information.