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Understanding Alternating Current Circuits and Impedance in RLC Systems

This chapter covers the fundamental concepts of alternating current (AC) circuits, focusing on AC voltage sources and the relationship between voltage and current over time. Key topics include the definition of period, frequency, and angular frequency, along with the concept of root-mean-square (RMS) voltage. The chapter explains the roles of inductors and capacitors in AC circuits, their reactance, and how they influence current flow. It also discusses RLC circuits, impedance, and phase relationships that occur during the interaction of resistors, inductors, and capacitors.

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Understanding Alternating Current Circuits and Impedance in RLC Systems

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  1. Chapter 33 Alternating-Current Circuits

  2. AC Sources • Voltage varies with time • Period (T)—time it takes to cycle once • Units of seconds • Frequency (f)—number of complete cycles per second • Units of Hz, 1/s • Angular frequency ()—rate at which the generator producing the voltage is spinning • Units of rad/s

  3. RMS Voltage • Average value of voltage over one cycle is zero • Voltage and current are described by the root-mean-square (RMS) value • Square the function • Take the average value • Take the square root

  4. Inductors in AC circuits • Current is constantly changing in an AC circuit • Inductors fight a change in current • The higher the frequency, the faster the current changes, and the more the inductor fights back • Inductive reactance (XL)—effective resistance of an inductor • Units of Ohms () • Dependent on the frequency of the signal For a simple L circuit

  5. Capacitors in AC Circuits • Capacitors do not represent a true break in an AC circuit • Since current changes direction, capacitors do not stop the flow • Capacitors will resist more as they charge up, the longer the current stays in one direction • Capacitive Reactance (XC)—effective resistance of the capacitor • Units of Ohms • Inversely proportional to frequency of current For a simple C circuit

  6. RLC Circuits • When a resistor, inductor, and capacitor are hooked in series, total resistance to current flow is called impedance (Z)

  7. RLC Circuits • Voltage and current do not reach max values at the same time due to the capacitor and inductor • Sine curves are out of phase by an angle (), called the phase angle • When  is negative, voltage trails the current • When  is positive, voltage leads the current • When  is 0, they are in phase, and current is at its maximum possible value for that voltage • Frequency at which this occurs is called the resonant frequency

  8. Purely resistive circuits  = 0 Purely capacitive circuits  = -90 Purely inductive circuits  = 90 RC Circuits  = negative, between -90 and 0 RL Circuits  = positive, between 0 and 90 RLC Circuits  = negative if XC>XL  = positive if XC<XL  = zero if XC = XL Phase relationships

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