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Fundamentals Of Physics
Found in: Page 935
Fundamentals Of Physics

Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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Short Answer

Figure 31-24 shows three situations like those in Fig. 31-15. Is the driving angular frequency greater than, less than, or equal to the resonant angular frequency of the circuit in (a) situation 1, (b) situation 2, and (c)situation 3?

  1. The angular frequency in situation 1 is less than the resonant angular frequency of the circuit.
  2. The angular frequency in situation 2 is equal to the resonant angular frequency of the circuit.
  3. The angular frequency in situation 3 is greater than the resonant angular frequency of the circuit.
See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: The given data

Figure 31-24 shows three situations of frequencies.

Step 2: Understanding the concept of resonance frequency

When the current leads the emf, then the angular frequency is less and vice versa. This case of current leading indicates flowing through a capacitor. If current lags the emf, this is when the current flows through an inductor.

Step 3: a) Calculation of the angular frequency in situation 1

The current I leads the driving emf E, so angular frequency is less than the resonant frequency.

Step 4: b) Calculation of the angular frequency in situation 2

The current I and the driving emf E have the same phase difference, so angular frequency is equal to the resonant frequency.

Step 5: c) Calculation of the angular frequency in situation 3

The current I is larger than the driving emf E, so the angular frequency is greater than the resonant frequency.

Most popular questions for Physics Textbooks

Remove the capacitor from the circuit in Figure and set R=200 Ω,L=230mH, fd=60.0 Hz, and εm=36.0 V. (a)What is the Z? (b)What is the ϕ? (c)What is the I? (d) Draw a phasor diagram.

Fig: A single-loop circuit containing a resistor, a capacitor, and an inductor. A generator, represented by a sine wave in a circle, produces an alternating emf that establishes an alternating current; the directions of the emf and current are indicated here at only one instant.

An alternating source with a variable frequency, a capacitor with capacitance C, and a resistor with resistance R are connected in series. Figure gives the impedance Z of the circuit versus the driving angular frequency ωd; the curve reaches an asymptote of 500 Ω, and the horizontal scale is set by (ωd )s=300 rad/s. The figure also gives the reactance XC for the capacitor versus ωd. What are (a) What is R ?(b) What is C ?

An ac generator provides emf to a resistive load in a remote factory over a two-cable transmission line. At the factory a stepdown transformer reduces the voltage from its (rms) transmission value Vt to a much lower value that is safe and convenient for use in the factory. The transmission line resistance is R=0.30 Ω/cable, and the power of the generator is P=250 kW. If Vt=80 kV, what are (a) the voltage decreases V along the transmission line and (b) the rate ΔV at which energy is dissipated in the line as thermal energy? If Vt=80 kV, what are (c) V and (d) ΔV ? If Vt=80 kV, what are (e) V and (f) Pd?

Consider the circuit shown in Fig. 31-40. With the switch S1 closed and the other two switches open, the circuit has a time constant τC . With the switch S2 closed and the other two switches open, the circuit has a time constant τL . With the switch S3 closed and the other two switches open, the circuit oscillates with a period T. Show that T=2πτCτL

For Fig. 31-35, show that the average rate at which energy is dissipated in resistance R is a maximum when R is equal to the internal resistance r of the ac generator. (In the text discussion we tacitly assumed that r = 0.)
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