A series RLC AC circuit has resistance R = 2.10 102 Ω, inductance L = 0.800 H, capacitance C = 3.50 µF, frequency f = 60.0 Hz, and maximum voltage ΔVmax = 3.00 102 V. (a) Find the impedance. Ω (b) Find the maximum current in the circuit. A (c) Find the phase angle. °
A series RLC AC circuit has resistance R = 2.10 102 Ω, inductance L = 0.800 H, capacitance C = 3.50 µF, frequency f = 60.0 Hz, and maximum voltage ΔVmax = 3.00 102 V. (a) Find the impedance. Ω (b) Find the maximum current in the circuit. A (c) Find the phase angle. °
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REMARKS Because the circuit is more capacitive than inductive (XC > XL), ? is negative. A negative phase angle means that the current leads the applied voltage. Notice also that the sum of the maximum voltages across the elements is ΔVR + ΔVL + ΔVC = 314 V, which is much greater than the maximum voltage of the generator, 150 V. The sum of the maximum voltages is a meaningless quantity because when alternating voltages are added, both their amplitudes and their phases must be taken into account. We know that the maximum voltages across the various elements occur at different times, so it doesn't make sense to add all the maximum values. The correct way to "add" the voltages is through an equation used specifically for that purpose.
QUESTION In an RLC circuit, the impedance must always be
QUESTION In an RLC circuit, the impedance must always be
either greater or less than the resistance, depending on frequency.less than or equal to the resistance. greater than or equal to the resistance.
PRACTICE IT
Use the worked example above to help you solve this problem. A series RLC AC circuit has resistance R = 2.10 102 Ω, inductance L = 0.800 H, capacitance C = 3.50 µF, frequency f = 60.0 Hz, and maximum voltage ΔVmax = 3.00 102 V.
(a) Find the impedance.
Ω
(b) Find the maximum current in the circuit.
A
(c) Find the phase angle.
°
(d) Find the maximum voltages across the elements.
Ω
(b) Find the maximum current in the circuit.
A
(c) Find the phase angle.
°
(d) Find the maximum voltages across the elements.
| ΔVR, max = | V |
| ΔVL, max = | V |
| ΔVC, max = | V |
EXERCISEHINTS: GETTING STARTED | I'M STUCK!
Analyze a series RLC AC circuit for which R = 270 Ω, L = 0.600 H, C = 22.5 µF, f = 50.0 Hz, and ΔVmax = 325 V.
(a) Find the impedance.
Z = Ω
(b) Find the maximum current.
Imax = A
(c) Find the phase angle.
? = °
(d) Find the maximum voltages across the elements.
Z = Ω
(b) Find the maximum current.
Imax = A
(c) Find the phase angle.
? = °
(d) Find the maximum voltages across the elements.
| ΔVR, max = | V |
| ΔVL, max = | V |
| ΔVC, max = | V |
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