Homework 10M - Phasors and Filters
March 27th, 2017
Due Monday, April 3
A series RLC circuit has values of R = 67 ⌦, C = 22 µF, and L = 67 mH, and is driven
by an AC source with VRM S = 12 V and f = 81 Hz. When the voltage is 7.2 V across the
resistor, what is the voltage across the inductor? You may use preliminary results from the
supplemental lecture notes - you don’t have to do the whole problem from the beginning,
but make sure you understand how those preliminary results were derived, and modify them
in the right way for the di↵erences between the problem in the notes and this one.
A lowpass filter consists of a 6.03 µF capacitor and a 120 ⌦ resistor. First calculate the
cuto↵ frequency (it’s in the notes [10M], but please do it from the formula here and then
use the notes to check your result). Then calculate the attenuation of the filter at 150 Hz
and 50 Hz.
For problems 3-6: A parallel RLC circuit consists of a 3.7 mH inductor, a 4.7 µF capacitor,
and a 1.4 ⌦ resistor driven at 150 Hz.
Draw the circuit - remember that it is a parallel circuit (all components).
Calculate the reactance of each component at the driving frequency (f = 150 Hz, but you
probably want !).
Draw the phasor diagram for the circuit, noting that the voltage, not the current, is common
to all three components since it is a parallel circuit. Be sure to label each of the three
phasors, and put each current in the right position with a fixed voltage.
Calculate the impedance Z for this circuit. Remember that you need to use the AC version
of Ohm’s law appropriately, since the current is common.
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