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

� � � � � � � 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

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

✄ ✞ ☎ ✟ ✆ ✁ ✠ ✌ ✒ ✖ LR Circuit (cont’d) ✡✦☛ ✍✏✎ ✓★✧

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

❃❄ ✳ ❇ ✳ ❆ ❅ ❁ ✞ ☎ ✟ ✆ ❂ ✲ ☎ AC Signals v(t) T V t −V T = period (s) f = = frequency (Hz) =2 f = angular frequency (rad/s) V = amplitude 2V = peak-to-peak amplitude

❂ ❅ ✆ P ❅ ❉❊ ❆ ▲ ❂ ✭ ✲ ❃❄ ✭ ✳ ☎ ❙ ✓ ❈ ✭ ✆ ❚ ❯ ✭ ✆ ✝ ❱ ❲ ✝ ❲ ❂ ❈ ✾ ❉❊ ❂ ❳ ✳ ❈❉❊ ❋ ● ❍ ☛ ❇ ❆ ▲ ❁ ✞ ☎ ✟ ✭ ✂ ❖ ❨ ❅ ✓ ✭ ❨ ❁ ✞ ☎ ✟ ✆ ❂ ✲ ❃❄ ✳ ☎ ❈❉❊ Root-Mean-Squared Amplitude ☎◆▼ ■❑❏ For , ❆❘◗ 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

☎ ✲ ✑ ✚ ☎ ❩ ✳ ❃❄ ✑ ❁ ❂ ✆ ☎ ❩ ✳ ❃❄ ✆ ✑ ❉ ☎ ❩ ✳ ❃❄ ✲ ✄ ✆ ❩ ✠ ✳ ❃❄ ✲ ✠ ✑ ❂ ✆ ✲ ✁ ✑ ❁ ✝ ✆ ✑ ❁ ✌ ✁ ✆ Resistive Load Connected to an AC Generator Rotation of v , i R R i R phasors at ω I R rate d V R v i R R ε i R t I R R v R V R ω d t

❞ ❂ ✪ ❩ ✳ ☛ ✆ ❬ ❫ ☎ ❩ ✳ ✰✱✲ ❬ ❫ ❬ ✆ ✪ ☎ ❩ ✳ ✲ ✱ ✰ ✖ ❬ ❪ ❭ ❅ ✡ ❬ ❂ ✙ ✥ ☎ ✚ ❝ ✾ ❇ ✫ ☎ ❩ ✳ ❜ ❃❄ ✲ ❬ ✄ ✆ ❬ ✟ ❴ ✍ ✜ ✣ ✥ ☎ ✜ ✥ ✍ ✍❵ ❁ ☎✚ ✚ ✜ ✥ ✆ ❩ ✳ ✩ ✪ ✆ ❬ ❁ ✪ ✆ ❬ ☎ ❬ ❩ ✳ ❃❄ ❬ ❂ ✆ ❬ ❁ ❂ ✲ ✲ ❬ ❂ ✪ ❩ ❃❄ ✳ ✆ ✂☎ ✩ ✰✱✲ ✂ ✆ ❬ ✚ ☎ ❩ ✳ ❬ Capacitive Load Connected to an AC Generator v i , Rotation of C C I C phasors at ω V v rate C C d i C I C ε i C C t v V C C ω d t i C ✞◆❛ The current leads the voltage by 90

❞ ✲ ❫ ✔ ✿ ❀ ✰ ✱ ✳ ❂ ❩ ☎ ❫ ✔ ✆ ✳ ✔ ✽ ✘ ✿ ✽ ❂ ✔ ✳ ❩ ✘ ❀ ✼ ✰✱✲ ✳ ❩ ☎ ✆ ✌ ❩ ✙ ✌ ❜ ✔ ✆ ✄ ✔ ✲ ❃❄ ✳ ✟ ❩ ☎ ✌ ❇ ✾ ❝ ✚ ❛ ✄ ❵ ✣ ✂❡ ✜ ☎✚ ❁ ✍ ✍ ✞ ✥ ✜ ☎✥ ✣ ✜ ✍ ✼ ✆ ☎ ✚ ✔ ❂ ✆ ✘ ✔ ❁ ✆ ☎ ✂ ✂ ✲ ❩ ✳ ❃❄ ✲ ✔ ❂ ✆ ✔ ❁ ✘ ☎ ❃❄ ❂ ❩ ✳ ❃❄ ✲ ❏ ✘ ✔ ✳ ✆ ✂ ✔ ✚ ✂ ❏ ✆ ✔ ✚ ☎ ❩ ☎ ε i L Inductive Load Connected to an AC Generator L v , L L V I L i The current lags the voltage by 90 L v L i L t i L v L ω d t V L I L rate phasors at Rotation of ω d

❉ ❛ ❉ � ✁ ❉ ✁ ❢ ❢ � ✁ 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 = 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?