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Conceptual questions

When a wire is connected between the two ends of a solenoid, the resulting circuit can oscillate like an RLC circuit. Describe what causes the capacitance in this circuit.

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Describe what effect the resistance of the connecting wires has on an oscillating LC circuit.

This creates an RLC circuit that dissipates energy, causing oscillations to decrease in amplitude slowly or quickly depending on the value of resistance.

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Suppose you wanted to design an LC circuit with a frequency of 0.01 Hz. What problems might you encounter?

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A radio receiver uses an RLC circuit to pick out particular frequencies to listen to in your house or car without hearing other unwanted frequencies. How would someone design such a circuit?

You would have to pick out a resistance that is small enough so that only one station at a time is picked up, but big enough so that the tuner doesn’t have to be set at exactly the correct frequency. The inductance or capacitance would have to be varied to tune into the station however practically speaking, variable capacitors are a lot easier to build in a circuit.

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Problems

In an oscillating RLC circuit, R = 5.0 Ω , L = 5.0 mH , and C = 500 μ F . What is the angular frequency of the oscillations?

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In an oscillating RLC circuit with L = 10 mH , C = 1.5 µ F , and R = 2.0 Ω , how much time elapses before the amplitude of the oscillations drops to half its initial value?

6.9 ms

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What resistance R must be connected in series with a 200-mH inductor of the resulting RLC oscillating circuit is to decay to 50 % of its initial value of charge in 50 cycles? To 0.10 % of its initial value in 50 cycles?

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Additional problems

Show that the self-inductance per unit length of an infinite, straight, thin wire is infinite.

proof Outside, B = μ 0 I 2 π r Inside, B = μ 0 I r 2 π a 2 U = μ 0 I 2 l 4 π ( 1 4 + ln R a ) So, 2 U I 2 = μ 0 l 2 π ( 1 4 + ln R a ) and L =

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Two long, parallel wires carry equal currents in opposite directions. The radius of each wire is a , and the distance between the centers of the wires is d . Show that if the magnetic flux within the wires themselves can be ignored, the self-inductance of a length l of such a pair of wires is

L = μ 0 l π ln d a a .

( Hint : Calculate the magnetic flux through a rectangle of length l between the wires and then use L = N Φ / I .)

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A small, rectangular single loop of wire with dimensions l , and a is placed, as shown below, in the plane of a much larger, rectangular single loop of wire. The two short sides of the larger loop are so far from the smaller loop that their magnetic fields over the smaller fields over the smaller loop can be ignored. What is the mutual inductance of the two loops?

The figure shows a rectangular loop of wire. The length of the rectangle is l and width is a. On both sides of the rectangle are wires parallel to its length. They are a distance d away from the rectangle. Current I1 flows through both in opposites directions.

M = μ 0 l π ln d + a d

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Suppose that a cylindrical solenoid is wrapped around a core of iron whose magnetic susceptibility is x . Using [link] , show that the self-inductance of the solenoid is given by

L = ( 1 + x ) μ 0 N 2 A l ,

where l is its length, A its cross-sectional area, and N its total number of turns.

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The solenoid of the preceding problem is wrapped around an iron core whose magnetic susceptibility is 4.0 × 10 3 . (a) If a current of 2.0 A flows through the solenoid, what is the magnetic field in the iron core? (b) What is the effective surface current formed by the aligned atomic current loops in the iron core? (c) What is the self-inductance of the filled solenoid?

a. 100 T; b. 2 A; c. 0.50 H

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Questions & Answers

Figure, shows a pencil partially immersed in a cup of water. Why does the pencil appear to be ?bent
Motion
Abdulrahman
what is heat capacity
Sessy Reply
joule
Abdikadir
defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin
Abdikadir
formula of acid hydride
Suman Reply
what is mass
Exildah Reply
mass is the amount of staff made up an object
Van
physic is anatural science that deals about scleral
Abdilahi
mass is accelaration divided force
Abdilahi
mass is force divided by acceleration
Van
Is the amout of matter contain in a body
El-shaddai
what is the volume of a human being
Collins Reply
Why does the lines of force not touch each other 🇲🇲
Gbemisola Reply
what is physics
Exildah
physics is the study of matter and energy and the interaction between them
Van
physics is the study of energy and matter
Komolafe
what is unit
Rayyanu Reply
Please canu get more questions on electric field and electric flux please
Gbemisola
is electric field directly proportional to the squared of a distance
Benjamin Reply
No electric field is inversely proportional to the squared distance between the charges
Gbemisola
lets treat linear expansivity please
Ujah Reply
The bullet 2.00cm long is fired at 420/s and passes straight through a 10.0 cm thick board existing at 280 m/s.What is the average acceleration of the bullet through the board?
FAUSTINA
an unstretched spring is 12cm long .A load of 5N stretched it to 15cm .how long will it be under a load of 15N?
Morapeli
hi
Africa
hi
Benjamin
Benjamin how are u are u a freshman in the university
Africa
like 100 level
Africa
yes sir
Benjamin
l need a physics tutor
Benjamin
I think the best tutor is God and organic tutor in YouTube that guy is good
Africa
me too 100level
Africa
wow nice
Benjamin
from Nigeria and u
Africa
I am from Nigeria and u wow nice that something I use to always say
Africa
am from Ghana
Benjamin
ok
Africa
studying what
Africa
like to join the group hope am welcome
Komolafe
Compare the electric flux through the surface of a cube of side length a that has a charge q at its center to the flux through a spherical surface of radius a with a charge q at its center.
Shari Reply
please I want to know how to solve increase in length
Ujah
ok
Komolafe
Why a charged capacitor has potential difference but not emf
Gideon Reply
what is the dimension symbol of temperature?
Keren Reply
what is the dimension symbol of temperature?
Keren
what's the meaning of enthalpy in terms of latent heat, internal energy, phase change
Anthony Reply
Enthalpy is the degree ofdisorderlinessof a substance
Gbemisola
how to convert Kelvin to centigrade
Sangeetha Reply
what is the s, p, d, f in this table
Sangeetha
s, p, d, f in this table
Sangeetha
what kind of table this
Vengata
Periodic table
Gbemisola
what are waves
KENNETH Reply
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities
Abdikadir
Practice Key Terms 1

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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