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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

Maxwell's stress tensor is
Ami Reply
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Jaffar
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
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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