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Chapter 33

Chapter 33. Alternating-Current Circuits. 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

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Chapter 33

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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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