AC Circuits LR Circuit LRC Circuit AC Signals Resistive Load - - PowerPoint PPT Presentation

▶

Aug 18, 2022 217 likes •334 views

AC Circuits LR Circuit LRC Circuit AC Signals Resistive Load Connected to an AC Generator Capacitive Load Connected to an AC Generator Inductive Load Connected to an AC Generator Home work

SLIDE 1

AC Circuits

LR Circuit
LRC Circuit
AC Signals
Resistive Load Connected to an AC Generator
Capacitive Load Connected to an AC Generator
Inductive Load Connected to an AC Generator
Home work

SLIDE 2

LR Circuit

✁

IR-L

✂ ✄ ✂☎ ✆ ✝ ✄ ✞ ☎ ✟ ✆ ✁ ✠ ✡☞☛ ✌ ✍✏✎ ✑ ✒ ✓✕✔ ✖ ✗ ✆ ✘ ✠ ✙ ☎✚ ✛ ✍✜✢ ✣✤ ☎✥ ✣ ☎

SLIDE 3

LR Circuit (cont’d)

✄ ✞ ☎ ✟ ✆ ✁ ✠ ✡✦☛ ✌ ✍✏✎ ✒ ✓★✧ ✖

SLIDE 4

LRC Circuit

L C R S

✩ ✪✬✫ ✘ ✂ ✄ ✂☎ ✫ ✄ ✠ ✆ ✝ ✘ ✂✮✭ ✩ ✂☎ ✭ ✫ ✠ ✂ ✩ ✂ ☎ ✫ ☛ ✪ ✩ ✆ ✝ ✩ ✞ ☎ ✟ ✆ ✯ ✍✏✎ ✑ ✒ ✓ ✭ ✔ ✰✱✲ ✞✴✳✶✵ ☎ ✫ ✷ ✟ ✳✸✵ ✆ ✹ ✺ ✺ ✺ ✺ ✻ ✳ ✭ ✌ ✼ ✽ ✠ ✾ ✘ ✿ ❀ ✭ ✆ ✹ ✺ ✺ ✺ ✺ ✻ ☛ ✘ ✪ ✌ ✼ ✽ ✠ ✾ ✘ ✿ ❀ ✭

SLIDE 5

AC Signals

v(t) t V −V T

❁ ✞ ☎ ✟ ✆ ❂ ✲ ❃❄ ✳ ☎

T = period (s) f =

❅ ❆

= frequency (Hz)

✳

=2

❇

f = angular frequency (rad/s) V = amplitude 2V = peak-to-peak amplitude

SLIDE 6

Root-Mean-Squared Amplitude

❂ ❈❉❊ ❋

☛ ■❑❏ ❆ ▲ ❁ ✞ ☎ ✟ ✭ ✂ ☎◆▼ ❖ ❅ ✓ ✭

For

❁ ✞ ☎ ✟ ✆ ❂ ✲ ❃❄ ✳ ☎

,

❂ ❈ ❉❊ ✆ P ❅ ❆❘◗ ❆ ▲ ❂ ✭ ✲ ❃❄ ✭ ✳ ☎ ❙ ❅ ✓ ✭ ✆ ❚ ❯ ✭ ✆ ✝ ❱ ❲ ✝ ❲ ❂

For example, consider the common 110-V, 60-Hz line voltage V

❈❉❊

= 110 V V =

❳ ✾

V

❈ ❉❊

= 156 V V

❨ ❨

= 2V = 312 V v(t) = V sin

✳

t = (156 V) sin 2

❇

(60 Hz)t

SLIDE 7

Resistive Load Connected to an AC Generator

iR

R

i

R

v , v

R

iR V

R

IR iR v

R

ω

d t

IR V

R

ω

d

Rotation of phasors at rate ε R t

✁ ✌ ❁ ✑ ✆ ✝ ❁ ✑ ✆ ✁ ❉ ✲ ❃❄ ✳ ❩ ☎ ✆ ❂ ✑ ✲ ❃❄ ✳ ❩ ☎ ✚ ✑ ✆ ❁ ✑ ✠ ✆ ❂ ✑ ✠ ✲ ❃❄ ✳ ❩ ☎ ✆ ✄ ✲ ❃❄ ✳ ❩ ☎

SLIDE 8

Capacitive Load Connected to an AC Generator

iC ,

C

v

C

i iC v

C

V

C

IC ω

d t

V

C

IC v

C

iC ω

d

Rotation of phasors at rate ε t C

❁ ❬ ✆ ❂ ❬ ✲ ❃❄ ✳ ❩ ☎ ✩ ❬ ✆ ✪ ❁ ❬ ✆ ✪ ❂ ❬ ✲ ❃❄ ✳ ❩ ☎ ✚ ❬ ✆ ✂ ✩ ❬ ✂☎ ✆ ✳ ❩ ✪ ❂ ❬ ✰✱✲ ✳ ❩ ☎ ✆ ❂ ❬ ✡ ❅ ❭ ❪ ❬ ✖ ✰ ✱ ✲ ✳ ❩ ☎ ✆ ❂ ❬ ❫ ❬ ✰✱✲ ✳ ❩ ☎ ❫ ❬ ✆ ☛ ✳ ❩ ✪ ✙ ✪ ✥ ❴ ✥ ✜ ✚ ☎✚ ❁ ✍❵ ✍ ✥ ✜ ☎ ✥ ✣ ✜ ✍ ✞◆❛ ✟ ✚ ❬ ✆ ✄ ❬ ✲ ❃❄ ❜ ✳ ❩ ☎ ✫ ❇ ✾ ❝

The current leads the voltage by 90

❞

SLIDE 9

Inductive Load Connected to an AC Generator

iL ω

d t L

v , L i V

L

IL v

L

iL ω

d

Rotation of phasors at rate V

L

IL iL v

L

ε t L

❁ ✔ ✆ ❂ ✔ ✲ ❃❄ ✳ ❩ ☎ ✂ ✚ ✂ ☎ ✆ ❁ ✔ ✘ ✆ ❂ ✔ ✘ ✲ ❃❄ ✳ ❩ ☎ ✚ ✔ ✆ ❏ ✂ ✚ ✔ ✆ ❂ ✔ ✘ ❏ ✲ ❃❄ ✳ ❩ ☎ ✂ ☎ ✆ ✌ ✼ ✽ ❂ ✔ ✳ ❩ ✘ ✿ ❀ ✰✱✲ ✳ ❩ ☎ ✆ ✌ ✼ ✽ ❂ ✔ ❫ ✔ ✿ ❀ ✰ ✱ ✲ ✳ ❩ ☎ ❫ ✔ ✆ ✳ ❩ ✘ ✙ ✄ ✣ ✂❡ ✜ ☎✚ ❁ ✍ ❵ ✍ ✥ ✜ ☎✥ ✣ ✜ ✍ ✞ ❛ ✟ ✚ ✔ ✆ ✄ ✔ ✲ ❃❄ ❜ ✳ ❩ ☎ ✌ ❇ ✾ ❝

The current lags the voltage by 90

❞

SLIDE 10

Homework Set 15 - Due Wed. Feb. 18

Read Section 23.6
Do problem 23.33 in the text and the following problems:
1. What resistance R should be connected in series with an inductor L = 220 mH and capacitance C

= 12.0

❢

F for the maximum charge on the capacitor to decay to 99.0% of its initial value in 50.0 cycles?

2. A 50.0

❛

resistor is connected to an ac generator with

✁ ❉

= 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is (a) 1.00 kHz and (b) 8.00 kHz?

3. A 1.50

❢

capacitor is connected to an ac generator with

✁ ❉

= 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is (a) 1.00 kHz and (b) 8.00 kHz?

4. A 50.0 mH inductor is connected to an ac generator with

✁ ❉