Download Understanding AC Circuits & Electromagnetic Waves: RLC Series Circuits - Prof. Pradeep Kum and more Study notes Physics in PDF only on Docsity! 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 Δv = ΔVmax sin 2πƒt Δv is the instantaneous voltage ΔVmax is the maximum voltage of the generator ƒ is the frequency at which the voltage changes, in Hz 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 max0.707 2 rms I I I= = max max0.707 2 rms V V V Δ Δ = = Δ Power Revisited The average power dissipated in resistor in an AC circuit carrying a current I is 2 av rmsI 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 ΔVR,rms = Irms R Also applies to the maximum values of v and i 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, XC will be in ohms Ohm’s Law for a capacitor in an AC circuit ΔVC,rms = Irms XC 1 2 ƒC X Cπ = 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° HITT In an AC series circuit the capacitive reactance is 200 Ω and frequency is 100 Hz. What is the capacitance? a. 3.2 μF b. 6.28 μF c. 8.0 μF d. 50.0 μF 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° Impedance of a Circuit The impedance, Z, can also be represented in a phasor diagram 2 2( ) tan L C L C Z R X X X X R φ = + − − = Impedance and Ohm’s Law Ohm’s Law can be applied to the impedance ΔVmax = Imax Z This can be regarded as a generalized form of Ohm’s Law applied to a series AC circuit
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© 2003 Thomson - Brooks Cole
Summary of Circuit Elements,
Impedance and Phase Angles
0°
-90°
+90°
Negative,
between —90° and 0°
Positive,
between 0° and 90°
Negative if X- > X;,
Positive if X¢< X;,
