GoBack Series RLC Circuit - Phasors AC Circuits • Series RLC Circuit - Let’s analyze the following circuit. Phasors • • Phasor Analysis (A Single Moment in Time) • Finding Peak Current in RLC - Circuit • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits PHYS102 AC Circuits - Phasors – slide 1 Series RLC Circuit - Phasors AC Circuits • Series RLC Circuit - Let’s analyze the following circuit. Phasors • • Phasor Analysis (A Single Moment in Time) R • Finding Peak Current in RLC - Circuit • Impedance • Current and Driving Voltage VP sin(ωt) Root-Mean-Square L Transforming Voltage C Amplitudes - AC - Circuits Calculate the peak current through the circuit • PHYS102 AC Circuits - Phasors – slide 1 Series RLC Circuit - Phasors AC Circuits • Series RLC Circuit - Let’s analyze the following circuit. Phasors • • Phasor Analysis (A Single Moment in Time) R • Finding Peak Current in RLC - Circuit • Impedance • Current and Driving Voltage VP sin(ωt) Root-Mean-Square L Transforming Voltage C Amplitudes - AC - Circuits Calculate the peak current through the circuit • We need to keep track of the phase differences ◦ PHYS102 AC Circuits - Phasors – slide 1 Series RLC Circuit - Phasors AC Circuits • Series RLC Circuit - Let’s analyze the following circuit. Phasors • • Phasor Analysis (A Single Moment in Time) R • Finding Peak Current in RLC - Circuit • Impedance • Current and Driving Voltage VP sin(ωt) Root-Mean-Square L Transforming Voltage C Amplitudes - AC - Circuits Calculate the peak current through the circuit • We need to keep track of the phase differences ◦ PHASORS! PHYS102 AC Circuits - Phasors – slide 1 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits The voltage across the resistor is represented by the phasor • above since the driving voltage is sinusoidal. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits The current is in phase with the voltage across the resistor. • PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits The current is in phase with the voltage across the resistor. • PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits The voltage across an inductor leads the current by π/2. • PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VLP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits The voltage across an inductor leads the current by π/2. • PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VLP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits The voltage across a capacitor lags behind the current by • π/2. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VLP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - VCP Circuits The voltage across a capacitor lags behind the current by • π/2. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VLP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - VCP Circuits Apply Kirchhoff’s Loop rule to find a relationship between all • the voltages. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VLP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - VCP Circuits Summing the phasors for the voltage across the capacitor and • inductor. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving VLP - VCP Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits Summing the phasors for the voltage across the capacitor and • inductor. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit I • Impedance • Current and Driving VLP - VCP Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits Summing the phasors for the voltage across the resistor and • capacitor/inductor. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit ϕ • Impedance I • Current and Driving VLP - VCP Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits Summing the phasors for the voltage across the resistor and • capacitor/inductor. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit ϕ • Impedance I • Current and Driving VLP - VCP Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits The length of the resultant phasor represents the peak voltage • supplied by the AC Voltage source. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit ϕ • Impedance I • Current and Driving VLP - VCP Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits Finding relationships between the peak current in the circuit • and the peak voltages is now a trigonometry problem. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit ϕ • Impedance I • Current and Driving VLP - VCP Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits NOTE: The driving peak voltage is out of phase with the peak • current through the circuit. PHYS102 AC Circuits - Phasors – slide 2 Phasor Analysis (A Single Moment in Time) AC Circuits • Series RLC Circuit - Phasors VP • Phasor Analysis (A Single Moment in Time) VRP • Finding Peak Current in RLC - Circuit ϕ • Impedance I • Current and Driving VLP - VCP Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits − − tan ϕ = VLP VCP = χL χc • VRP R 2 2 VP = V +(VLP VCP ) q RP − PHYS102 AC Circuits - Phasors – slide 2 Finding Peak Current in RLC - Circuit AC Circuits • Series RLC Circuit - Phasors 2 • Phasor Analysis (A 2 Single Moment in Time) VP = VRP +(VLP VCP ) • Finding Peak Current q − in RLC - Circuit • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits PHYS102 AC Circuits - Phasors – slide 3 Finding Peak Current in RLC - Circuit AC Circuits • Series RLC Circuit - Phasors 2 • Phasor Analysis (A 2 Single Moment in Time) VP = VRP +(VLP VCP ) • Finding Peak Current q − in RLC - Circuit VRP = IP R • Impedance • Current and Driving Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits PHYS102 AC Circuits - Phasors – slide 3 Finding Peak Current in RLC - Circuit AC Circuits • Series RLC Circuit - Phasors 2 • Phasor Analysis (A 2 Single Moment in Time) VP = VRP +(VLP VCP ) • Finding Peak Current q − in RLC - Circuit VRP = IP R • Impedance • Current and Driving VLP = IP χL Voltage Root-Mean-Square Transforming Voltage Amplitudes - AC - Circuits PHYS102 AC Circuits - Phasors – slide 3 Finding Peak Current in RLC - Circuit AC Circuits • Series RLC Circuit - Phasors 2 • Phasor Analysis (A 2 Single Moment in Time) VP = VRP +(VLP VCP ) • Finding Peak Current q − in RLC - Circuit VRP = IP R • Impedance • Current and Driving VLP = IP χL Voltage Root-Mean-Square VCP = IP χc Transforming Voltage Amplitudes - AC - Circuits PHYS102