LECTURE 26 Deadline for this week’s homework

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LECTURE 26 Deadline for this week’s homework assignment is extended until Friday, March 30, after lecture Pick up lecture notes

RLC circuits with generators Lecture 25 Lecture 26 NO generator With generator Decaying oscillations Sustained oscillations

Problem 1 A resistor and an inductor are connected in series with an AC generator whose emf is given by E(t) = Eo cos(wt). Find (a) the effective impedance Z(w) of the circuit (b) the phase difference between the emf E(t) and the current I(t). R Definition of Z:

Problem 2 A resistor and an inductor are now connected in parallel with the generator E(t) = Eo cos(wt). Calculate for this configuration the effective impedance Z(w) of the circuit (b) the phase difference between the emf E(t) and the current I(t). Definition of Z:

Complex impedance formalism GOAL: Reduce AC problems to DC problems Typical problem: generator signal given: E(t) = Eo cos(wt), need to find the current I(t) = Io(w)cos(wt-d) Note: Choose complex form for E Look for a current of the form where Io(w) is complex:

Complex impedance formalism Voltage across R Just like in the DC case! Voltage across L Looks like a “resistor” with Complex impedance ZL Voltage across C Looks like a “resistor” with complex impedance ZC ALL RULES FOR DC CIRCUITS APPLY WITHIN THE COMPLEX IMPEDANCE FORMALISM

Problem 2’ Use the complex impedance formalism to find: the effective impedance Z(w) of the circuit (b) the phase difference between the emf E(t) and the current I(t).

Problem 3 Calculate the total effective impedance for the following circuit: (b) Calculate the phase shift between E(t) and the current I(t) flowing through the generator.

Problem 4 Find the frequency at which the current is the largest in the series RLC circuit. Problem 5 Show that in the parallel configuration, the current flowing through the generator has a minimum.