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Download PHYS 222 Worksheet 24 More AC Circuits
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PHYS 222 Worksheet 24 – More AC Circuits Supplemental Instruction Iowa State University Useful Equations RLC Circuit: Phasors: ALWAYS draw the diagram!! Z ( X L X C )2 R 2 E (VL VC )2 VR 2 E IZ tan X L XC R Leader: Course: Instructor: Date: Alek Jerauld PHYS 222 Dr. Paula Herrera-Siklódy 3/22/12 Related Problems 1) You have a 200 ohm resistor, a 0.400-H inductor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. For this R-L circuit graph V, VR, and VL versus t for t = 0 to t = 50.0 ms. The current is given by I = I cos(wt) so v = V cos(ωt + φ). (Draw the phasor diagram) E E I 0.1342 A 2 2 Z L R VL IX L 13.42 V VR 30 V 2) You have a 200-Ω resistor, a 0.400-H inductor, a 6.00-μF capacitor and a voltage source that has a voltage amplitude of 30.0 V and an angular frequency of 250 rad/s. The resistor, inductor, capacitor, and voltage source are connected to form an L-R-C series circuit. The current is given by I = I cos(ωt), so v = V cos(ωt + φ). Graph v, VR, VL, and VC as a function of time for t = 0 to t = 27 ms. (Draw the phasor diagram) E E 0.05 A 2 Z 1 2 L R C VL IX L 5 V I VR 30 V VC IX C 33.3 V 3) An ac source whose rms voltage is 80 V is in series with a 100- ohm resistor and a capacitor, whose reactance is 200 ohms at the frequency of the source. The instantaneous current, when the voltage of the source is zero and is increasing, is closest to: (a) zero (b) 0.23 A (c) 0.16 A (d) 0.45 A (d) 0.32 A 200 1.107 rad 100 v 0 RI cos t cos t 0 tan 1 t cos 1 (0) / 2 t i I max cos(t ) 2.678 rad E 80 2 2.678 cos t cos 0.4525 A Z 2002 1002 4) An R-L-C series circuit is constructed using a 175-ohm resistor, a 12.5-µF capacitor, and an 8.00-mH inductor, all connected across an ac source having a variable frequency and a voltage amplitude of 25.0 V. (a) At what angular frequency will the impedance be smallest? Z min X L X C 0 X L X C L 1 C 1 3160 rad / s LC (b) What is the impedance at this frequency? Z min X L XC 2 R 2 R 175 (c) At the angular frequency in part A, what is the maximum current through the inductor? E 25 I 0.143 A Z 175 (d) At the angular frequency in part A, find the potential difference across the ac source, the resistor, the capacitor, and the inductor at the instant that the current is equal to one-half its greatest positive value. i I max cos t 0.143 0.143cos 3160t 2 t 0.000331 vL IX L cos t / 2 3.13 V vC IX C cos t / 2 3.13 V vR IR cos t 12.5 V v E cos t 12.5 V