hing to use phaso 60.0 Hz and the resistor has a resistance of 47.5 0. eering students are diagrams to analyze RLC They are given the following phasor diagram, and they the AC powwer source AV = 25.0 V AVnax AVg= 20.0 V AVc=15.0 V dotermine the following

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Chapter33: Alternating Current Circuits
Section: Chapter Questions
Problem 33.60AP
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Engineering students are learning to use phasor diagrams to analyze RLC series circuits. They are given the following phasor diagram, and they are told that the AC power source has a frequency of
60.0 Hz and the resistor has a resistance of 47.5 Q.
AV = 25.0 V
AV
max
AVR= 20.0 V
AVc= 15.0 V
The students are then asked to determine the following.
(a) the maximum voltage AV,
(in V) across the series RLC combination
max
22.36
V
(b) the phase angle o (in degrees)
25.56
Referring to the right triangle formed by adding the three phasors, which angle is the phase angle? How can you find the value of this angle from the values for the magnitude of the phasors? °
(c) the maximum current (in A) in the circuit
.42103
A
(d) the total impedance (in N) of the circuit
53.1067
(e) the capacitance (in µF
.74456
Express the capacitive reactance in terms of the voltage across the capacitor and the maximum current and then in terms of the capacitance and frequency. How can we determine the
capacitance from these two expressions? Don't forget to convert F to µF. uF
(f) the inductance (in H)
.1575
(g) the average power (in W) delivered to the circuit
.4207
Transcribed Image Text:Engineering students are learning to use phasor diagrams to analyze RLC series circuits. They are given the following phasor diagram, and they are told that the AC power source has a frequency of 60.0 Hz and the resistor has a resistance of 47.5 Q. AV = 25.0 V AV max AVR= 20.0 V AVc= 15.0 V The students are then asked to determine the following. (a) the maximum voltage AV, (in V) across the series RLC combination max 22.36 V (b) the phase angle o (in degrees) 25.56 Referring to the right triangle formed by adding the three phasors, which angle is the phase angle? How can you find the value of this angle from the values for the magnitude of the phasors? ° (c) the maximum current (in A) in the circuit .42103 A (d) the total impedance (in N) of the circuit 53.1067 (e) the capacitance (in µF .74456 Express the capacitive reactance in terms of the voltage across the capacitor and the maximum current and then in terms of the capacitance and frequency. How can we determine the capacitance from these two expressions? Don't forget to convert F to µF. uF (f) the inductance (in H) .1575 (g) the average power (in W) delivered to the circuit .4207
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