Transcription of Chapter 21: RLC Circuits
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Chapter 21: RLC Circuits
PHY2054: Chapter 211 Chapter 21: RLC CircuitsPHY2054: Chapter 212 Voltage and Current in RLC Circuits AC emf source: driving frequency f If circuit contains only R + emf source, current is simple If L and/or C present, current is notin phase with emf Z, shown later()sinmmmiItIZ = =sinmt =2f =()()sincurrent amplitudemmmiI tIRR ===PHY2054: Chapter 213AC Source and Resistor Only Driving voltage is Relation of current and voltage Current is in phasewith voltage ( = 0)i R~sinmmmiIt IR ==sinmt =/iR =PHY2054: Chapter 214AC Source and Capacitor Only Voltage is Differentiate to find current Rewrite using phase (check this!) Relation of current and voltage Capacitive reactance : Current leads voltage by 90 sinmqCt =i C~/cosCidqdt CVt ==sinCmqvtC ==()sin90 CiCVt =+ ()sin90mmmCiItIX =+ =1/CXC =()1/CXC =PHY2054: Chapter 215AC Source and Inductor Only Voltage is Integrate di/dt to find current: Rewrite using phase (check this!)
PHY2054: Chapter 21 19 Power in AC Circuits ÎPower formula ÎRewrite using Îcosφis the “power factor” To maximize power delivered to circuit ⇒make φclose to zero Max power delivered to load happens at resonance E.g., too much inductive reactance (X L) can be cancelled by increasing X C (e.g., circuits with large motors) 2 P ave rms=IR rms ave rms rms rms cos
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