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chapter21

# chapter21 - Chapter 21 Alternating Current Circuits and...

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Chapter 21 Alternating Current Circuits and Electromagnetic Waves

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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 Δv = ΔV max sin 2 ƒt Δv is the instantaneous voltage ΔV max is the maximum voltage of the generator ƒ 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

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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 Where i is the instantaneous current The heating effect produced by an AC current with a maximum value of I max is not the same as that of a DC current of the same value The maximum current occurs for a small amount of time 2 i R
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 Alternating voltages can also be discussed in terms of rms values max max 0.707 2 rms I I I max max 0.707 2 rms V V V

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Power Revisited The average power dissipated in resistor in an AC circuit carrying a current I is 2 av rms I R
Notation Note

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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 ΔV R,rms = I rms 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

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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 When ƒ is in Hz and C is in F, X C will be in ohms Ohm’s Law for a capacitor in an AC circuit ΔV C,rms = I rms X C 1 2 ƒ C X C

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Inductors in an AC Circuit Consider an AC circuit with a source and an inductor
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chapter21 - Chapter 21 Alternating Current Circuits and...

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