Explanation 1) Concept: By using the concept of energy stored in the capacitor, energy stored in the inductor, the energy supplied by the emf device, and the energy dissipated in resistor, we can prove all the parts. 2) Formula: i) Energy stored in capacitor, U E = q 2 2 C ii) Energy stored in inductor, U B = 1 2 L i 2 iii) Rate of energy supply by driving emf device, P ϵ = i ϵ Where, i = I s i n ( ω d - ϕ ) and ϵ = ϵ m s i n ω d t iv) Rate with which energy dissipates, P R = i 2 R 3) Given: An RLC circuit with period T . 4) Calculations: a) We know that charge q is a periodic function of t with period T . As U E = q 2 2 C So U E must also be the periodic function of t Thus, the energy stored in the capacitor does not change. b) Since, current i is also a periodic of t with period T . As U B = 1 2 L i 2 So U B must also be the periodic function of t Thus, the energy stored in inductor does not change. c) The energy supplied by the emf device over one cycle is U E = ∫ 0 T P ϵ d t = I ϵ m ∫ 0 T s i n ⁡ ( ω d t - ϕ ) s i n ⁡ ( ω d t ) d t U E = I ϵ m ∫ 0 T [ s i n ⁡ ( ω d t ) c o s ϕ - cos ⁡ ω d t s i

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Concept explainers

Electromagnets

The word "electromagnet" is composed of two words, ‘electro’ and ‘magnet’. It is a type of magnet in which an electric current helps in the generation of a magnetic field. Electromagnets usually consist of two major parts, wire and a coil around which th…

Question

Chapter 31, Problem 89P

To determine

To show:

a) Energy stored in the capacitor does not change

b) Energy stored in the inductor does not change

c) Driving emf device supplies energy 12TϵmI cosϕ

d) Resistor dissipates energy 12TRI2

e) Quantities found in part c and part d are equal

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 31, Problem 88P

Chapter 31, Problem 90P

Students have asked these similar questions

Using Table 17-4, determine the approximate temperature of metal that has formed a dark blue color.

A positively charged disk has a uniform charge per unit area σ. dq R P x The total electric field at P is given by the following. Ek [2 - x (R² + x2) 1/2 Sketch the electric field lines in a plane perpendicular to the plane of the disk passing through its center.

Consider a closed triangular box resting within a horizontal electric field of magnitude E = 8.02 104 N/C as shown in the figure below. A closed right triangular box with its vertical side on the left and downward slope on the right rests within a horizontal electric field vector E that points from left to right. The box has a height of 10.0 cm and a depth of 30.0 cm. The downward slope of the box makes an angle of 60 degrees with the vertical. (a) Calculate the electric flux through the vertical rectangular surface of the box. kN · m2/C(b) Calculate the electric flux through the slanted surface of the box. kN · m2/C(c) Calculate the electric flux through the entire surface of the box. kN · m2/C

Chapter 31 Solutions

Fundamentals of Physics Extended

Ch. 31 - Figure 31-19 shows three oscillating LC circuits...Ch. 31 - Figure 31-20 shows graphs of capacitor voltage vc...Ch. 31 - Prob. 3Q Ch. 31 - What values of phase constant in Eq. 31-12 allow...Ch. 31 - Curve a in Fig. 31-21 gives the impedance Z of a...Ch. 31 - Prob. 6Q Ch. 31 - Prob. 7Q Ch. 31 - The values of the phase constant for four...Ch. 31 - Prob. 9Q Ch. 31 - Figure 31-24 shows three situations like those of...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

a) Energy stored in the capacitor does not change b) Energy stored in the inductor does not change c) Driving emf device supplies energy 1 2 T ϵ m I c o s ϕ d) Resistor dissipates energy 1 2 T R I 2 e) Quantities found in part c and part d are equal

Solution Summary: The author explains how the concept of energy stored in the capacitor, inductor, and resistor can prove all the parts.

Concept explainers

To show:

a) Energy stored in the capacitor does not change

b) Energy stored in the inductor does not change

c) Driving emf device supplies energy 12TϵmI cosϕ

d) Resistor dissipates energy 12TRI2

e) Quantities found in part c and part d are equal

Want to see the full answer?

Chapter 31 Solutions

a) Energy stored in the capacitor does not change b) Energy stored in the inductor does not change c) Driving emf device supplies energy 1 2 T ϵ m I c o s ϕ d) Resistor dissipates energy 1 2 T R I 2 e) Quantities found in part c and part d are equal

Solution Summary: The author explains how the concept of energy stored in the capacitor, inductor, and resistor can prove all the parts.

Concept explainers

To show: a) Energy stored in the capacitor does not change b) Energy stored in the inductor does not change c) Driving emf device supplies energy 12TϵmI cosϕ d) Resistor dissipates energy 12TRI2 e) Quantities found in part c and part d are equal

Want to see the full answer?

Chapter 31 Solutions

To show:

a) Energy stored in the capacitor does not change

b) Energy stored in the inductor does not change

c) Driving emf device supplies energy 12TϵmI cosϕ

d) Resistor dissipates energy 12TRI2

e) Quantities found in part c and part d are equal