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UF PHY 2054 - Alternating Current Circuits and Electromagnetic Waves

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Chapter 21 Alternating Current Circuits and Electromagnetic Waves AC Circuit An AC circuit consists of a combination of circuit elements and an AC generator or source The output of an AC generator is sinusoidal and varies with time according to the following equation v Vmax sin 2 t v is the instantaneous voltage Vmax is the maximum voltage of the generator is the frequency at which the voltage changes in Hz Resistor in an AC Circuit Consider a circuit consisting of an AC source and a resistor The graph shows the current through and the voltage across the resistor The current and the voltage reach their maximum values at the same time The current and the voltage are said to be in phase More About Resistors in an AC Circuit The direction of the current has no effect on the behavior of the resistor The rate at which electrical energy is dissipated in the circuit is given by 2 i R where i is the instantaneous current the heating effect produced by an AC current with a maximum value of Imax is not the same as that of a DC current of the same value The maximum current occurs for a small amount of time rms Current and Voltage The rms current is the direct current that would dissipate the same amount of energy in a resistor as is actually dissipated by the AC current I rms I max 2 0 707 I max Alternating voltages can also be discussed in terms of rms values Vrms Vmax 2 0 707 Vmax Power Revisited The average power dissipated in resistor in an AC circuit carrying a current I is av I 2 rms R Ohm s Law in an AC Circuit rms values will be used when discussing AC currents and voltages AC ammeters and voltmeters are designed to read rms values Many of the equations will be in the same form as in DC circuits Ohm s Law for a resistor R in an AC circuit VR rms Irms R Also applies to the maximum values of v and i Capacitors in an AC Circuit Consider a circuit containing a capacitor and an AC source The current starts out at a large value and charges the plates of the capacitor There is initially no resistance to hinder the flow of the current while the plates are not charged As the charge on the plates increases the voltage across the plates increases and the current flowing in the circuit decreases More About Capacitors in an AC Circuit The current reverses direction The voltage across the plates decreases as the plates lose the charge they had accumulated The voltage across the capacitor lags behind the current by 90 Capacitive Reactance and Ohm s Law The impeding effect of a capacitor on the current in an AC circuit is called the capacitive reactance and is given by 1 XC 2 C When is in Hz and C is in F X C will be in ohms Ohm s Law for a capacitor in an AC circuit VC rms Irms XC Inductors in an AC Circuit Consider an AC circuit with a source and an inductor The current in the circuit is impeded by the back emf of the inductor The voltage across the inductor always leads the current by 90 Inductive Reactance and Ohm s Law The effective resistance of a coil in an AC circuit is called its inductive reactance and is given by XL 2 L When is in Hz and L is in H XL will be in ohms Ohm s Law for the inductor VL rms Irms XL The RLC Series Circuit The resistor inductor and capacitor can be combined in a circuit The current in the circuit is the same at any time and varies sinusoidally with time Current and Voltage Relationships in an RLC Circuit The instantaneous voltage across the resistor is in phase with the current The instantaneous voltage across the inductor leads the current by 90 The instantaneous voltage across the capacitor lags the current by 90 Phasor Diagrams To account for the different phases of the voltage drops vector techniques are used Represent the voltage across each element as a rotating vector called a phasor The diagram is called a phasor diagram Phasor Diagram for RLC Series Circuit The voltage across the resistor is on the x axis since it is in phase with the current The voltage across the inductor is on the y since it leads the current by 90 The voltage across the capacitor is on the y axis since it lags behind the current by 90 Phasor Diagram cont The phasors are added as vectors to account for the phase differences in the voltages VL and VC are on the same line and so the net y component is VL VC Vmax From the Phasor Diagram The voltages are not in phase so they cannot simply be added to get the voltage across the combination of the elements or the voltage source Vmax VR2 VL VC 2 VL VC tan VR angle between the current is the phase and the maximum voltage The equations also apply to rms values Impedance of a Circuit The impedance Z can also be represented in a phasor diagram Z R2 X L X C 2 X L XC tan R Impedance and Ohm s Law Ohm s Law can be applied to the impedance Vmax Imax Z This can be regarded as a generalized form of Ohm s Law applied to a series AC circuit Summary of Circuit Elements Impedance and Phase Angles Nikola Tesla 1865 1943 Inventor Key figure in development of AC electricity High voltage transformers Transport of electrical power via AC transmission lines Beat Edison s idea of DC transmission lines Problem Solving for AC Circuits Calculate as many unknown quantities as possible For example find XL and XC Be careful of units use F H Apply Ohm s Law to the portion of the circuit that is of interest Determine all the unknowns asked for in the problem Power in an AC Circuit No power losses are associated with pure capacitors and pure inductors in an AC circuit In a capacitor during one half of a cycle energy is stored and during the other half the energy is returned to the circuit In an inductor the source does work against the back emf of the inductor and energy is stored in the inductor but when the current begins to decrease in the circuit the energy is returned to the circuit Power in an AC Circuit cont The average power delivered by the generator is converted to internal energy in the resistor Pav Irms VR Irms Vrms cos cos is called the power factor of the circuit Phase shifts can be used to maximize power outputs Resonance in an AC Circuit Resonance occurs at the frequency o where the current has its maximum value To achieve maximum current the impedance must have a minimum value This occurs when XL XC Then o 1 2 LC Resonance cont Theoretically if R 0 the current would be infinite at resonance Tuning a radio …


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UF PHY 2054 - Alternating Current Circuits and Electromagnetic Waves

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