Textbook Question
A series ac circuit contains a 250-Ω resistor, a 15-mH inductor, a 3.5-μF capacitor, and an ac power source of voltage amplitude 45 V operating at an angular frequency of 360 rad/s.What is the power factor of this circuit?
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Ch 31: Alternating Current
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 31, Problem 20
In an L-R-C series circuit, the components have the following values: L = 20.0 mH, C = 140 nF, and R = 350 Ω.The generator has an rms voltage of 120 V and a frequency of 1.25 kHz. Determine (a) the power supplied by the generator and (b) the power dissipated in the resistor.
Verified step by step guidance1
First, calculate the angular frequency (ω) of the circuit using the formula ω = 2πf, where f is the frequency of the generator. Substitute f = 1.25 kHz into the formula to find ω.
Next, determine the inductive reactance (X_L) using the formula X_L = ωL, where L is the inductance. Substitute the values of ω and L = 20.0 mH to find X_L.
Calculate the capacitive reactance (X_C) using the formula X_C = 1/(ωC), where C is the capacitance. Substitute the values of ω and C = 140 nF to find X_C.
Find the total impedance (Z) of the circuit using the formula Z = √(R² + (X_L - X_C)²). Substitute the values of R, X_L, and X_C to find Z.
Finally, calculate the power supplied by the generator using the formula P = (V_rms²)/Z, where V_rms is the rms voltage of the generator. Then, calculate the power dissipated in the resistor using the formula P_R = (V_rms²)/R.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Impedance in L-R-C Circuits
Impedance is the total opposition a circuit offers to the flow of alternating current, combining resistance (R), inductive reactance (XL), and capacitive reactance (XC). In an L-R-C series circuit, impedance (Z) is calculated using Z = √(R² + (XL - XC)²), where XL = 2πfL and XC = 1/(2πfC). Understanding impedance is crucial for determining the current and power in the circuit.
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08:40
Impedance in AC Circuits
Power in AC Circuits
In AC circuits, power is calculated using the formula P = Vrms * Irms * cos(φ), where φ is the phase angle between voltage and current. The real power dissipated in the resistor is given by P = I²R, where I is the current through the resistor. This concept helps in calculating both the power supplied by the generator and the power dissipated in the resistor.
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05:37Power in AC Circuits
Resonance in L-R-C Circuits
Resonance occurs in an L-R-C circuit when the inductive reactance equals the capacitive reactance (XL = XC), resulting in maximum current flow. At resonance, the impedance is minimized, and the circuit behaves purely resistive. Understanding resonance is essential for analyzing the circuit's behavior at different frequencies, especially when calculating power.
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05:23Resonance in Series LRC Circuits
Related Practice
Textbook Question
An L-R-C series circuit with L = 0.120 H, R = 240 Ω, and C = 7.30 μF carries an rms current of 0.450 A with a frequency of 400 Hz. What are the phase angle and power factor for this circuit?
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Textbook Question
An L-R-C series circuit is connected to a 120-Hz ac source that has Vrms = 80.0 V. The circuit has a resistance of 75.0 Ω and an impedance at this frequency of 105 Ω. What average power is delivered to the circuit by the source?
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Textbook Question
A resistor with R = 300 Ω and an inductor are connected in series across an ac source that has voltage amplitude 500 V. The rate at which electrical energy is dissipated in the resistor is 286 W. What is (a) the impedance Z of the circuit; (b) the amplitude of the voltage across the inductor; (c) the power factor?
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Textbook Question
The power of a certain CD player operating at 120 V rms is 20.0 W. Assuming that the CD player behaves like a pure resistor, find the maximum instantaneous power.
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Textbook Question
You have a 200-Ω resistor, a 0.400-H inductor, and a 6.00-μF capacitor. They are connected to form an L-R-C series circuit. What is the current amplitude?