Homework 10M - Phasors and Filters March 27th, 2017 Phys 162 1. Name: 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. 2. 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. 3. Draw the circuit - remember that it is a parallel circuit (all components). 4. Calculate the reactance of each component at the driving frequency (f = 150 Hz, but you probably want !). 5. 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. 6. 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. s✓ ◆ ✓ ◆ 1 1 2 1 1 2 = + Z R L C
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