Aula5 PDF - Circuits Analysis 2024-2025

2024-2025 Análise de Circuitos Circuits Analysis 41990 Class 5: Node and Loop Analysis, Thevenin and Norton Theorems in AC Recap – Impedance and Admittance Symbol Impedance Admittance Resistance R...

2024-2025 Análise de Circuitos Circuits Analysis 41990 Class 5: Node and Loop Analysis, Thevenin and Norton Theorems in AC Recap – Impedance and Admittance Symbol Impedance Admittance Resistance R 𝑍! = 𝑅 𝑌! = 1%𝑅 Inductance L 𝑍" = 𝑗𝜔𝐿 𝑌" = 1%𝑗𝜔𝐿 Capacitance C 𝑍# = 1%𝑗𝜔𝐶 𝑌# = 𝑗𝜔𝐶 [email protected] 2 Recap - Complex Numbers and Phasor Example 1: Calculate the impedance (Z) and admittance (Y) of an inductor in a circuit with sinusoidal excitation, assuming the following: 𝜔 = 10 𝑟𝑎𝑑/𝑠 Tip: 𝐿 = 0.6 𝐻 1 1 = −𝑗 𝑍" = 𝑗𝜔𝐿 = 𝑗6 Ω 𝑌" = ≈ −𝑗0.167 𝑆 𝑗 𝑗𝜔𝐿 Example 2: Calculate the load voltage on the inductor, assuming the circuit has a voltage source and a resistor (10 Ω) in series: 𝑣$ = 10 cos(10𝑡) 𝑍" 𝑗6 60𝑗(10 − 𝑗6) 600𝑗 + 360 𝑉" = 𝑉% = 10 = = ≈ 𝟐. 𝟔𝟒𝟕 + 𝟒. 𝟒𝟏𝒋 𝑽 𝑅 + 𝑍" 10 + 𝑗6 (10 + 𝑗6)(10 − 𝑗6) 136 [email protected] 3 Recap - Complex Numbers and Phasor Example 3: Represent the following voltage phasor in the exponential form: 𝑉" = −5 − 4𝑗 𝑉 Im II Quadrant I Quadrant 𝑉" = 𝑟 = 5& + 4& ≈ 𝟔. 𝟒 𝑽 -5 4 Re Ð 𝑉" = 𝜃 = tan'( ≈ 0.675 ± 𝜋 𝑟𝑎𝑑 5 (III Q) = 𝜋 + 0.675 ≈ 𝟐𝟏𝟗° -4 III Quadrant IV Quadrant 𝑽𝑳 = 𝟔. 𝟒𝒆𝒋𝟐𝟏𝟗° [email protected] 4 Nodal Analysis Example in AC Example 4: Calculate VL: b c ib Rc Rbb iS RS Rbe Aiib Lce Cce RL VL e 𝑖% = 5 𝑐𝑜𝑠 (2 10) 𝑡) 𝑚𝐴 𝑅% = 1𝑘Ω 𝑅, = 25 Ω 𝐿,+ = 0.5 𝐻 𝐴- = 100 𝑅** = 1𝑘Ω 𝑅" = 75 Ω 𝐶,+ = 5 𝜇𝐹 𝑅*+ = 3𝑘Ω −1000 900𝑗 𝑉. = 4𝑉 𝐼. = 1𝑚𝐴 𝑉# = + ≈ 7.43𝑒 ()/° 𝑉 𝑉" = 5.57𝑒 ()/° 𝑉 181 181 [email protected] 5