**RLC Circuit Analysis**A generator connected to an RLC circuit has an RMS voltage of 160 V and an RMS current of 36 mA.**Problem Statement****Part A:**If the resistance in the circuit is 3.1 kΩ and the capacitive reactance is 6.7 kΩ, what is the inductive reactance of the circuit?**Instructions:**Express your answers using two significant figures. Enter your answers numerically separated by a comma.**Input Field:**- \( X_L = \) [Enter Value] kΩ**Buttons Available:**- Submit- Request Answer**Navigation:**- Return to Assignment- Provide FeedbackThis exercise is designed to deepen understanding of RLC circuit operations, emphasizing reactance calculations based on provided values of resistance, capacitive, and inductive reactance.

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Answered: A generator connected to an RLC circuit…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter33: Inductors And Ac Circuits

Section: Chapter Questions

Problem 38PQ

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Neon signs require 12-kV for their operation. A transformer is to be used to change the voltage from 220-V (rms) ac to 12-kV (rms) ac. What must the ratio be of turns in the secondary winding to the turns in the primary winding? (b) What is the maximum rms current the neon lamps can draw if the fuse in the primary winding goes off at 0.5 A? (C) How much power is used by the neon sign when it is drawing the maximum current allowed by the fuse in the primary winding?
In a damped oscillating circuit the energy is dissipated In the resistor. The Q-factor Is a measure of the persistence of the oscillator against the dissipative loss. (a) Prove that for a ligt1y danced circuit the energy, U, in the circuit decreases according to the following equation. du dt =2u,where= R 2L (b) Using the definition of the Q-factor as energy divided by the loss over the next cycle, prove that Q-factor of a lightly damped oscillator as defined in this problem is Q= U begin U onecycle = 1 R L C c (Hint: For (b), to obtain Q, divide E at the beginning of one cycle by the change E over the next cycle.)
Electrosurgical units (ESUs) supply high-frequency electricity from resonant RLC circuits to cut. coagulate, or otherwise modify biological tissue. (a) Find the resonant frequency of an ESU with an inductance of L = 1.25 H and a capacitance of 47.0 nF. (b) Calculate the capacitance required for a resonant frequency of 1.33 MHz.
In addition to phasor diagrams showing voltages such as in Figure 32.15, we can draw phasor diagrams with resistance and reactances. The resultant of adding the phasors is the impedance. Draw to scale a phasor diagram showing Z, XL, XC, and for an AC series circuit for which R = 300 , C = 11.0 F, L = 0.200 H, and f = 500/ Hz.
When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P30.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin t represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is Emax=0nAImax. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P30.8
A resistor and capacitor are connected in series across an ac generator. The emf of the generator is given by V(t)=V0cost , where V0=120V , =120rad/s , R=400and C=400F.(a)What is the impedance of the circuit? (b) What is the amplitude of the current through the resistor? (C) Write an expression for the current through the resistor. (d) Write expressions representing the voltages across the resistor and across the capacitor.
In a series RLC circuit with a maximum current of 0.250 A, an AC source with Vmax= 115 V operating at 60.0 Hz is connected to a 325-mH inductor, a 7.50-F capacitor, and a resistor with unknown resistance R. Draw a phasor diagram for this circuit, including the current, the potential difference across each of the circuit elements, and the source emf. Draw your diagram with the current phasor pointing upward along the vertical axis.
An RLC circuit consists of a 150- resistor, a 21.0-F capacitor, and a 466-mH inductor connected in series with a 120-V, 60.0-Hz power supply. (a) What is the phase angle between the current and the applied voltage? (b) Which reaches its maximum earlier, the current or the voltage?
A 100-mH inductor is connected across the emf of the preceding problem. (a) What is the reactance of the Inductor? (b) Write an expression for the current through the inductor.
A 2.0-F capacitor is charged to a potential difference of 12.0 V and then connected across a 0.40-mH inductor. What is the current in the circuit when the potential difference across the capacitor is 6.0 V?
(a) Sketch a graph of the phase angle for an RLC series circuit as a function of angular frequency from zero to a frequency much higher than the resonance frequency. (b) Identify the value of at the resonance angular frequency 0. (c) Prove that the slope of the graph of versus at the resonance point is 2Q/0.
An RLC series circuit consists of a 10 resistor, an 8.0F capacitor, and a 50-mH inductor. A 110-V (rms) source of variable frequency is connected across the combination. What is the power output of the source when its frequency is set to one-half the resonant frequency of the circuit?

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