1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
BlackZzzverrR [31]
3 years ago
11

A resonant circuit using a 286-nFnF capacitor is to resonate at 18.0 kHzkHz. The air-core inductor is to be a solenoid with clos

ely packed coils made from 12.0 mm of insulated wire 1.1 mmmm in diameter. The permeability of free space is 4π×10−7T⋅m/A4π×10−7T⋅m/A.
How many loops will the inductor contain?
Physics
1 answer:
lukranit [14]3 years ago
4 0

Answer:

The inductor contains N = 523962.32 loops  

Explanation:

From the question we are told that

     The capacitance of the capacitor is  C =  286nF = 286 * 10^{-9} \  F

      The resonance frequency is  f = 18.0 kHz =  18*10^{3} Hz

       The diameter is  d =  1.1 mm = \frac{1.1 }{1000} = 0.00011 \ m

       The  of the air-core inductor is l = 12 \ m

        The permeability of free space is  \mu_o = 4 \pi *10^{-7} \ T \cdot m/A

 

Generally the inductance of this air-core inductor is mathematically represented as

              L =  \frac{\mu_o * N^2 \pi d^2}{4 l}

This inductance can also be mathematically represented as

               L = \frac{1}{w^2}

Where w is the angular speed mathematically given as

             w = 2 \pi f

So

            L =  \frac{1}{4 \pi ^2 f^2}

Now equating the both formulas for inductance

         \frac{\mu_o * N^2 \pi d^2}{4 l}  =  \frac{1}{4 \pi ^2 f^2}

making N the subject of  the formula

              N = \sqrt{\frac{1}{(2 \pi f)^2} * \frac{4 * l }{\mu_o * \pi d^2 C}  }

              N =  \frac{1}{2 \pi f} * \frac{2}{d} * \sqrt{\frac{l}{\pi * \mu_o * C} }

             

 Substituting value

            N =  \frac{1}{ 3.142  * 18*10^{3} * 0.00011 }  \sqrt{\frac{12}{ 3.142  * 4 \pi *10^{-7}* 286 *10^{-9}} }

              N = 523962.32 loops  

You might be interested in
A metal block suspended from a spring balance is submerged in water. You observe that the block displaces 55 cm3 of water and th
DiKsa [7]

Answer:

8977.7 kg/m^3

Explanation:

Volume of water displaced = 55 cm^3 = 55 x 10^-6 m^3

Reading of balance when block is immersed in water = 4.3 N

According to the Archimedes principle, when a body is immersed n a liquid partly or wholly, then there is a loss in the weight of body which is called upthrust or buoyant force. this buoyant force is equal to the weight of liquid displaced by the body.

Buoyant force = weight of the water displaced by the block

Buoyant force = Volume of water displaced x density of water x g

                        = 55 x 10^-6 x 1000 x .8 = 0.539 N

True weight of the body = Weight of body in water + buoyant force

m g = 4.3 + 0.539 = 4.839

m = 0.4937 kg

Density of block = mass of block / volume of block

= \frac{0.4937}{55\times10^{-6}}

Density of block = 8977.7 kg/m^3

4 0
3 years ago
10. A 25 kg apple cart is being pushed with an applied force of 115 N. The coefficient of friction between the ground and the ca
ziro4ka [17]

Answer:

1.1 m/s²

Explanation:

From the question,

F -mgμ = ma.................... Equation 1

Where F = applied force, m = mass of the apple cart, g = acceleration due to gravity, μ =  coefficient of friction., a = acceleration of the apple cart.

Given: F = 115 N, m = 25 kg,  μ  = 0.35

Constant: g = 10 m/s²

Substitute these values into equation 2

115-(25×10×0.35) = 25×a

115-87.5 = 25a

25a = 27.5

a = 27.5/25

a = 1.1 m/s²

8 0
3 years ago
A block lies on a horizontal frictionless surface and
zhenek [66]

Answer:

0.1 m

Explanation:

F = Force exerted on spring = 3 N

k = Spring constant = 60 N/m

x = Displacement of the block

As the energy of the system is conserved we have

Fx=\dfrac{1}{2}kx^2

\\\Rightarrow x=\dfrac{2F}{k}

\\\Rightarrow x=\dfrac{2\times 3}{60}

\\\Rightarrow x=0.1\ m

The position of the block is 0.1 from the initial position.

6 0
3 years ago
What would happen to the amount of matter on earth if mass were not conserved during changes of state?
attashe74 [19]
<span>earth would be thrown off its balance and nature would be in danger of too many resources and not enough resources </span>
4 0
3 years ago
Read 2 more answers
A 0.60 kg rubber ball has a speed of 2.0 m/s at point A, and kinetic energy of 7.5 J at point
aliina [53]
<span>Let's first off calculate the kinetic energy using the formula 1/2MV^2. Where the mass, M, is 0.6Kg. And speed, V, is 2. Hence we have 1/2 * 0.6 * 2^2 = 1.2J. Since kinetic energy is energy due to motion; hence at point B the rubber has a KE of 1.2J and not 7.5J. So I would say that only the Mass and speed is actually true; While it's kinetic energy is not true.</span>
7 0
3 years ago
Other questions:
  • An infinite plane of charge has surface charge density 7.2 μC/m^2. How far apart are the equipotential surfaces whose potential
    10·1 answer
  • Compare the strong and weak megnetic field
    10·1 answer
  • What principle do all modern cameras use to form images ?
    15·2 answers
  • A 1.2-kg ball drops vertically onto the floor, hitting with a speed of 25 m/s. Consider the impulse during this collision. Would
    9·1 answer
  • What happens when an ionic compound is melted?
    8·1 answer
  • Suggest three properties which magnesium chloride has because it is an ionic compound
    6·1 answer
  • WILL MARK BRAINLIEST PLS HELP
    10·1 answer
  • The surface tension of isopropanol in air has a value of 23.00 units and the
    6·2 answers
  • can someone help me answer this correctly in the next 20 minutes? I’ll give out a brainliest if you can answer it right :)
    13·1 answer
  • A student in the Biomechanics class has decided that she would like to make her arms
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!