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CourseNotes.52

# CourseNotes.52 - Problem 31.44 An alternating emf source...

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Problem 31.44 An alternating emf source with a variable frequency f d is connected in series with a 50 Ω resistor and a 20 μF capacitor. The emf amplitude is 12 V . (a) Draw a phasor diagram for phasor V R (the potential across the resistor) and phasor V C (the potential across the capacitor). (b) At what driving frequency f d do the two phasors have the same length? At that driving frequency, what are (c) the phase angle in degrees, (d) the angular speed at which the phasors rotate, and (e) the current amplitude? We will not draw the figure here in the notes, but it should look exactly like figure 31-14 (b) in the textbook except without the V L vector. The length of the V R and V C vectors is given by their Ohm’s law relations. V C = I X C V R = I R Setting these equal to each other and solving for the frequency gives IX C = IR 1 ω d C = R ω d = 1 RC Since the problem asks for the frequency and not the angular frequency, we need to divide by 2 Pi .
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