David Halliday, Robert Resnick
ISBN #9781119460138
11th Edition
4,175 Questions
Homework Questions
An LC oscillator is a fundamental resonant circuit in which energy continually shifts between the electric field of a capacitor and the magnetic field of an inductor. By applying conservation of energy or Kirchhoff’s loop rule, we derive the differential equation L d²q/dt² + (1/C)q = 0, whose solution reveals that the oscillations are harmonic with an angular frequency ? = 1/?(LC). The charge and current in the circuit oscillate sinusoidally, with the current leading the charge by a phase of 90°. Understanding these principles is key to designing devices such as radio tuners and filters in electronics.
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In Fig. $30-33$, a circular loop of wire $10 \mathrm{~cm}$ in diameter (seen edge-on) is placed with its normal $\vec{N}$ at an angle $\theta=30^{\circ}$ with the direction of a uniform magnetic field $\vec{B}$ of magnitude $0.50 \mathrm{~T}$. The loop is then rotated such that $\vec{N}$ rotates in a cone about the field direction at the rate 100 rev/min; angle $\theta$ remains unchanged during the process. What is the emf induced in the loop?
A certain elastic conducting material is stretched into a circular loop of $12.0 \mathrm{~cm}$ radius. It is placed with its plane perpendicular to a uniform 0.800 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of $75.0 \mathrm{~cm} / \mathrm{s} .$ What emf is induced in the loop at that instant?
In Fig. $30-34,$ a 120-turn coil of radius $1.8 \mathrm{~cm}$ and resistance $5.3 \Omega$ is coaxial with a solenoid of 220 turns/cm and diameter $3.2 \mathrm{~cm} .$ The solenoid current drops from $1.5 \mathrm{~A}$ to zero in time interval $\Delta t=25 \mathrm{~ms} .$ What current is induced in the coil during $\Delta t ?$
A wire loop of radius $12 \mathrm{~cm}$ and resistance $8.5 \Omega$ is located in a uniform magnetic field $\vec{B}$ that changes in magnitude as given in Fig. $30-35 .$ The vertical The loop's plane is perpendicular to $\vec{B}$. What emf is induced in the loop during time intervals (a) 0 to $2.0 \mathrm{~s}$, (b) $2.0 \mathrm{~s}$ to $4.0 \mathrm{~s}$, and (c) $4.0 \mathrm{~s}$ to $6.0 \mathrm{~s} ?$
In Fig. $30-36,$ a wire forms a closed circular loop, of radius $R=2.0 \mathrm{~m}$ and resistance $4.0 \Omega .$ The circle is centered on a long straight wire; at time $t=0,$ the current in the long straight wire is 5.0 A rightward. Thereafter, the current changes according to $i=5.0 \mathrm{~A}-\left(2.0 \mathrm{~A} / \mathrm{s}^{2}\right) t^{2}$. (The straight wire is insulated; so there is no electrical contact between it and the wire of the loop.) What is the magnitude of the current induced in the loop at times $t>0 ?$