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Common application of resonant circuits is correcting power factor in power electronics. A related citation from IEEE Transactions on Power Electronics reads: "Everyone knows that correcting power factor is the easiest and fastest way to save energy dollars". Most industrial loads as well as residential loads (washer, dryer, air conditioner, refrigerator, etc.) are powered by induction motors. Figure a) shows a simplified equivalent circuit of an inductive load. We intend to add a capacitor in parallel with the load as in figure b). We attempt to choose the capacitance value in such a fashion as to make the equivalent load impedance Zeg purely cesistive (i.e. real. The capacitor in figure b) is called the power factor correction (PFC) capacitor. inductive load (a motor) 16(t) inductive load with a PFC capacitor i(t) a) b) Vg(t) O Vs(t) Given w 377 rad/sec, L 29.1 mH, R-52, determine the value of the capacitance, C, in microfarads which is necessary to make Zeg of the resulting RLC circuit in figure b) purely resistive or real. Present 3 significant digits. Hint: This problem has an elegant analytical solution. Using MATLAB is equally welcome! There, one could vary capacitance from, say, O to 0.001 F, find the equivalent impedance, and then find the capacitance value at which the imaginary part of the impedance becomes exactly zero.

Common application of resonant circuits is correcting power factor in power electronics. A related citation from IEEE Transactions on Power Electronics reads: "Everyone knows that correcting power factor is the easiest and fastest way to save energy dollars". Most industrial loads as well as residential loads (washer, dryer, air conditioner, refrigerator, etc.) are powered by induction motors. Figure a) shows a simplified equivalent circuit of an inductive load. We intend to add a capacitor in parallel with the load as in figure b). We attempt to choose the capacitance value in such a fashion as to make the equivalent load impedance Zeg purely cesistive (i.e. real. The capacitor in figure b) is called the power factor correction (PFC) capacitor. inductive load (a motor) 16(t) inductive load with a PFC capacitor i(t) a) b) Vg(t) O Vs(t) Given w 377 rad/sec, L 29.1 mH, R-52, determine the value of the capacitance, C, in microfarads which is necessary to make Zeg of the resulting RLC circuit in figure b) purely resistive or real. Present 3 significant digits. Hint: This problem has an elegant analytical solution. Using MATLAB is equally welcome! There, one could vary capacitance from, say, O to 0.001 F, find the equivalent impedance, and then find the capacitance value at which the imaginary part of the impedance becomes exactly zero.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Another common application of resonant circuits is correcting power factor in power electronics. A related citation from IEEE Transactions on Power Electronics reads: "Everyone knows that correcting power factor is the easiest and fastest way to save energy dollars", Most industrial loads as well as residential loads (washer, dryer, air conditioner, refrigerator, etc.) are powered by induction motors. Figure a) shows a simplified equivalent circuit of an inductive load. We intend to add a capacitor in parallel with the load as in figure b). We attempt to choose the capacitance value in such a fashion as to make the equivalent load impedance Zg purely resistive (i.e. real. The capacitor in figure b) is called the power factor correction (PFC) capacitor. inductive load (a motor) i,(t) inductive load with a PFC capacitor i(t) a) b) Vs(t) O Vs(t) Given w = 377 rad/sec, L = 29.1 mH, R= 52, determine the value of the capacitance, C, in microfarads which is necessary to make Zeg of the resulting RLC circuit in figure b) purely resistive or real. Present 3 significant digits. Hint: This problem has an elegant analytical solution. Using MATLAB is equally welcome! There, one could vary capacitance from, say, 0 to 0.001 F, find the equivalent impedance, and then find the capacitance value at which the imaginary part of the impedance becomes exactly zero.
Transcribed Image Text:Another common application of resonant circuits is correcting power factor in power electronics. A related citation from IEEE Transactions on Power Electronics reads: "Everyone knows that correcting power factor is the easiest and fastest way to save energy dollars", Most industrial loads as well as residential loads (washer, dryer, air conditioner, refrigerator, etc.) are powered by induction motors. Figure a) shows a simplified equivalent circuit of an inductive load. We intend to add a capacitor in parallel with the load as in figure b). We attempt to choose the capacitance value in such a fashion as to make the equivalent load impedance Zg purely resistive (i.e. real. The capacitor in figure b) is called the power factor correction (PFC) capacitor. inductive load (a motor) i,(t) inductive load with a PFC capacitor i(t) a) b) Vs(t) O Vs(t) Given w = 377 rad/sec, L = 29.1 mH, R= 52, determine the value of the capacitance, C, in microfarads which is necessary to make Zeg of the resulting RLC circuit in figure b) purely resistive or real. Present 3 significant digits. Hint: This problem has an elegant analytical solution. Using MATLAB is equally welcome! There, one could vary capacitance from, say, 0 to 0.001 F, find the equivalent impedance, and then find the capacitance value at which the imaginary part of the impedance becomes exactly zero.
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