Good day !!! Ohm’s law for a complete alternating-current circuit Learning Objectives use phasor diagram to add and subtract voltage and electric current to get correct answers in direction. define impedance of the completed ac circuit , phase angle and power factor apply Ohm’s law for a complete alternating-current circuit for solving problems; Schedule Part 1: • Quiz questions • Terminology • New information about phasor diagram; • Individual work on Drawing a phasor diagram Part 2: • Derivation of Ohm's law & an impedance formula • Pair work on an impedance formula + Solving problems • Self assessment • Feedback Learning outcomes Self assessment By the end of this lesson you should able to: • understand new words, the meaning of During the lesson words and phrases used in this lesson. • draw a phase diagram for simple circuits Discussion + Individual work and the complex circuit. • derive Ohm's law to completed ac circuit All together and the formula for the impedance • apply impedance equation to complex Discussion + Pair circuits. work Ready for a quiz? Why? • to review the previous lesson’s concepts and knowledges https://quizizz.com/admin/quiz/5fcbac7ebe16bf001f9e4672?searchLocale= Terminology • phasor • phasor diagram • complete alternatingcurrent circuit • impedance • phase angle • Power factor ? ? Ohm’s law π πΌ= π R-resistance π πΌ= ππΆ XC = 1 ωC π πΌ= ππΏ XL =π€πΏ ππ −? ππ = πΌπππ₯ sin π€π‘ ππΏ−? ποΆ ο¦ i L ο½ Imax sin ο§ ωt ο ο· 2οΈ ο¨ ππΆ−? ποΆ ο¦ iC ο½ Imax sin ο§ ωt ο« ο· 2οΈ ο¨ 8 it−? it = iR = iL = iC i ο½ Imax sin ωt vt−? v = v R + vL + vC v = v R + vL + vC Phase difference between vt and it-? To find the phase difference between vt and it-? we will use phasor diagram What is a phasor diagram? What is a phasor diagram? Phasor diagram is a way of representing sinusoidal waveforms such that you can add and subtract them and get correct answers (counter clockwise) direction. ππ = πΌπππ₯ sin π€π‘ What is a phasor diagram? π ππ πΌπππ₯ ππ = πΌπππ₯ sin ππ‘ What is a phasor diagram? π πΌπππ₯ ππ = πΌπππ₯ sin ππ‘ ππ = πΌπππ₯ sin ππ‘ ποΆ ο¦ i L ο½ Imax sin ο§ ωt ο ο· 2οΈ ο¨ ποΆ ο¦ iC ο½ Imax sin ο§ ωt ο« ο· 2οΈ ο¨ Draw a phasor for every circuit 15 ππ = πΌπππ₯ sin ππ‘ ποΆ ο¦ i L ο½ Imax sin ο§ ωt ο ο· 2οΈ ο¨ ποΆ ο¦ iC ο½ Imax sin ο§ ωt ο« ο· 2οΈ ο¨ π½πππ π½πππ π°πππ π°πππ π°πππ π½πππ Draw a phasor for this circuit Combine the individual phasor diagrams together •A single phasor Imax is used to represent the current in each element Vmax ? a phasor for a complete alternatingcurrent circuit v = vR + vL + v C π½πππ = π½π³ π½π³ − π½πͺ π π½π³ π½πͺ π½π³ − π½πͺ π½πΉ π½πͺ π°πππ π π½πΉ π°πππ + π½πΉ π RLC series circuit • Derive equation vmax from the vector diagram 24 RLC series circuit • Derive equation Imax (current in an RLC) from the vector diagram Z is called the impedance of the circuit and it plays the role of resistance in the circuit, where Z οΊ R ο« ο¨ X L ο XC ο© 2 2 25 φ - phase angle Imax οVmax ο½ Z Z οΊ R ο« ο¨ X L ο XC ο© 2 2 impedance triangle • Derive equation π from the vector diagram φ - phase angle X L ο XC οΆ ο1 ο¦ ? φο½ tan ο§ ο· R ο¨ οΈ i ο½ Imax sin ωt cos φ? = R Z Power in AC circuit Imax οVmax ο½ Z Irms ο½ Imax 2 • The average power delivered by the generator is converted to internal energy in the resistor Pav = ½ Imax ΔVmax cos φ = IrmsΔVrms cos φ cos φ is called the power factor of the circuit • We can also find the average power in terms of R 2 2 ο V ο V 1 1 R ο¦ οΆ 2 2 max Pav ο½ I rms R ο½ I max R ο½ ο§ max ο· R ο½ 2 2ο¨ Z οΈ 2 R 2 ο« ο¨ X L ο X C ο©2 29 Pair work on ‘’ RLC series circuit’’ Instructions for pair work • • • • • Discuss in pair 2-3 min Complete your tasks and write explanation. Checking work Assess your skills (1-5 mark). CHECKING WORK RLC series circuit ? ? ? ? ? ? 33 RLC series circuit 1 4π 2 +? π€πΏ − π€πΆ π= π= 4π 2 ?+ (ππΏ −ππ‘π )2 = 4π 2 π= 2 1 2 + (π€πΏ?− ) 3π€πΆ 2 π 2 ?+ (ππ‘πΏ )2 = π 2 + (2π€πΏ) ? 1 2 ) π€πΆπ‘ π = π ?2 + ( = π 2 2 2 ? +( ) π€πΆ 34 assessment time • Please complete self assessment sheet Competency Terminology Theory Drawing phasor diagram Formula derivation Application of Ohm's law Practical mastery Maximum Your possible Score mark I understand words and the meaning of 5 words and phrases used in the lesson. I know Ohm's law for simple electrical 5 circuits and completed ac circuits. I can draw a phase diagram for simple 5 circuits and complex circuits. I can derive Ohm's law, the formula for 5 impedance I can apply Ohm's law to solve 5 problems. Total /25 What has been learned? -What remained unclear? -What is necessary to work on? - End of lesson • What has been learned? • -What remained unclear? • -What is necessary to work on? • Please complete past paper questions for homework. • Well done!!
