W9_parallel_resonance.eps

336 Week 9: Alternating Current Circuits

Homework for Week 9

Problem 1.

Physics Concepts

Make this week’s physics concepts summary as you work all of the problems in this week’s
assignment. Be sure to cross-reference each concept in the summary to the problem(s) they were
key to. Do the work carefully enough that you can (after it has been handed in and graded) punch
it and add it to a three ring binder for review and study come finals!

Problem 2.

C

+Qo

R

S1 (close at t=0)

L

At timet= 0 the capacitor in theLRCcircuit above has a chargeQ 0 and the current in the
wire isI 0 = 0 (there is no current in the wire).DeriveQ(t), and draw a qualitatively correct picture
ofQ(t) in the case that the oscillation is only weakly damped. Show all your work.

Problem 3.

VR

C VC

R

In the circuit above, the AC voltage isV 0 cos(ωt). Find:

a) The currentI(t) through the resistor and capacitor, assuming no current is diverted into the

branches on the right. Clearly identify the relative phase shiftδbetween the applied voltage

and the current.

b) The voltageVR(t) across the resistor. Factor your answer out so that it is in termsof the

dimensionlessωRC.

c) The voltageVC(t) across the capacitor.

This circuit is called ahigh-pass filter, one that delivers the maximumcurrentin the circuit only
whenωRC≫1 (so that the capacitor behaves like a “short” with very low reactance).

When the frequency islow, the capacitor acts like a gap, with very high reactance, and does not
permit current to flow. At this point the applied voltage drop acrossthe capacitor is maximal, and
this pair of tap points is sometimes used to help clean up a DC power supply by “shorting out”