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

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

3. 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:

4. 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:

5. 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:

6. 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

7. 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).

8. 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.

9. 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.