# 14.6 Rlc series circuits  (Page 2/4)

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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.

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.

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

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.

## Problems

In an oscillating RLC circuit, $R=5.0\phantom{\rule{0.2em}{0ex}}\text{Ω},L=5.0\phantom{\rule{0.2em}{0ex}}\text{mH},\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}C=500\phantom{\rule{0.2em}{0ex}}\mu \text{F}.$ What is the angular frequency of the oscillations?

In an oscillating RLC circuit with $L=10\phantom{\rule{0.2em}{0ex}}\text{mH},C=1.5\phantom{\rule{0.2em}{0ex}}µ\text{F},\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}R=2.0\phantom{\rule{0.2em}{0ex}}\text{Ω},$ how much time elapses before the amplitude of the oscillations drops to half its initial value?

6.9 ms

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

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

proof $\begin{array}{ccc}\hfill \text{Outside,}\phantom{\rule{1em}{0ex}}B& =\hfill & \frac{{\mu }_{0}I}{2\pi r}\phantom{\rule{0.5em}{0ex}}\text{Inside,}\phantom{\rule{1em}{0ex}}B=\frac{{\mu }_{0}Ir}{2\pi {a}^{2}}\hfill \\ \hfill U& =\hfill & \frac{{\mu }_{0}{I}^{2}l}{4\pi }\left(\frac{1}{4}+\text{ln}\phantom{\rule{0.2em}{0ex}}\frac{R}{a}\right)\hfill \\ \hfill \text{So,}\phantom{\rule{2em}{0ex}}\frac{2U}{{I}^{2}}& =\hfill & \frac{{\mu }_{0}l}{2\pi }\left(\frac{1}{4}+\text{ln}\phantom{\rule{0.2em}{0ex}}\frac{R}{a}\right)\phantom{\rule{0.5em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}L=\infty \hfill \end{array}$

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

$L=\frac{{\mu }_{0}l}{\pi }\phantom{\rule{0.2em}{0ex}}\text{ln}\phantom{\rule{0.2em}{0ex}}\frac{d-a}{a}.$

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

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?

$M=\frac{{\mu }_{0}l}{\pi }\phantom{\rule{0.2em}{0ex}}\text{ln}\phantom{\rule{0.2em}{0ex}}\frac{d+a}{d}$

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

$L=\frac{\left(1+x\right){\mu }_{0}{N}^{2}A}{l},$

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

The solenoid of the preceding problem is wrapped around an iron core whose magnetic susceptibility is $4.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}$ . (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

how does beryllium decay occur
Photon?
Umar
state the first law of thermodynamics
Its state that "energy can neither be created nor destroyed but can be transformed from one form to another. "
Ayodamola
what about the other laws can anyone here help with it please
Sandy
The second law of thermodynamics states that the entropy of any isolated system always increases. The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.
sahil
The first law is very simple to understand by its equation. The law states that "total energy in thermodynamic sytem is always constant" i.e d¶=du+dw where d¶=total heat du=internal energy dw=workdone... PLEASE REFER TO THE BOOKS FOR MORE UNDERSTANDING OF THE CONCEPT.
Elia
what is distance.?
what is physics?
Ali
Physics is a scientific phenomenon that deals with matter and its properties
Ayodamola
physics is the study of nature and science
John
Chater1to7
min
Physics is branch of science which deals with the study of matters in relation with energy.
Elia
What is differential form of Gauss's law?
help me out on this question the permittivity of diamond is 1.46*10^-10.( a)what is the dielectric of diamond (b) what its susceptibility
a body is projected vertically upward of 30kmp/h how long will it take to reach a point 0.5km bellow e point of projection
i have to say. who cares. lol. why know that t all
Jeff
is this just a chat app about the openstax book?
kya ye b.sc ka hai agar haa to konsa part
what is charge quantization
it means that the total charge of a body will always be the integral multiples of basic unit charge ( e ) q = ne n : no of electrons or protons e : basic unit charge 1e = 1.602×10^-19
Riya
is the time quantized ? how ?
Mehmet
What do you meanby the statement,"Is the time quantized"
Mayowa
Can you give an explanation.
Mayowa
there are some comment on the time -quantized..
Mehmet
time is integer of the planck time, discrete..
Mehmet
planck time is travel in planck lenght of light..
Mehmet
it's says that charges does not occur in continuous form rather they are integral multiple of the elementary charge of an electron.
Tamoghna
it is just like bohr's theory. Which was angular momentum of electron is intral multiple of h/2π
determine absolute zero
The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy
U can easily calculate work done by 2.303log(v2/v1)
Abhishek
Amount of heat added through q=ncv^delta t
Abhishek
Change in internal energy through q=Q-w
Abhishek
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
what is copper loss
this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.
Henry
it is the work done in moving a charge to a point from infinity against electric field
what is the weight of the earth in space
As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...
Prince
g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass
Jorge
Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...
Prince
Thats why it can't have a constant value of g ....
Prince
not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth
Jorge