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murzikaleks [220]
3 years ago
5

You are given a length (l) of wire that has radius (a)and are told to wind it into an inductor in the shape of a helix that has

a circular cross section of radius (r). The windings are to be as close together as possible without overlapping. Show that the self-inductance of this inductor is L = 1/4nrl/a.
Physics
1 answer:
LiRa [457]3 years ago
5 0

To solve this problem it is necessary to apply the concepts related to inductance on an inductor, which is mathematically described as:

L = \mu_0 n^2 A l

Where,

\mu_0= Permeability constant (Described as 'n' at the problem equation)

l = Length

A = Cross-sectional Area

n = No of turn per unit length

The number of turns N is given by

N = \frac{l}{2a}

The number of turns per unit length n is

n = \frac{N}{l} = \frac{1}{2a}

The relationship of the cable lengths starts from assuming that the length 'a' is less than the length 'r', and therefore the length of the wire d would be related by:

d = N(2\pi r)

d = \frac{l}{2a}2\pi r

d = \frac{\pi r}{a}l

Solving to obtain l,

l = \frac{ad}{\pi r}

Substituting at the first equation,

L = \mu_0 n^2 A l

L = \mu_0 (\frac{1}{2a})^2(\pi r^2)(\frac{ad}{\pi r})

L = \mu_0 (\frac{rd}{4a})

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cestrela7 [59]
The Asante was fhhbbd
3 0
3 years ago
A 0.614mole sample of ideal gas at 12degree occupies a volume of 4.32.what is the pressure of the gas
Kaylis [27]

Answer:

336.9520 atm

Explanation:

The Gas Equation is as follows;-

Pressure×Volume=Number of Moles × Universal Gas Constant ×Temperature(in Kelvin)

Given Parameters

Number of moles-0.614 mol

Temperature 12°C or 12+273.15 ie 285.15°F

Volume-4.32 L

Universal Gas Constant-8.314 J/mol·K

Pressure -?(in atm)

Plugging in all the values in the Gas Equation:-

Pressure=\frac{0.614 × 8.314× 285.15}{4.32}   atm

Pressure=336.9520 atm

3 0
3 years ago
How to determine the amount of resistance when two or more resistors are in parallel.
Elena L [17]

Answer: 1/R = 1/R1 + 1/R2+ ...+ 1/Rn

R is resistance of system in which there are resistors R1, R2 , ... Rn parallel.

3 0
3 years ago
Through what potential difference should electrons be accelerated so that their speed is 1.0 % of the speed of light when they h
omeli [17]

Answer:

Explanation:

Considering non - relativistic approach : ----

Speed of electron = 1 % of speed of light

= .01 x 3 x 10⁸ m /s

= 3 x 10⁶ m /s

Kinetic energy of electron = 1/2 m v²

= .5 x 9.1 x 10⁻³¹ x ( 3 x 10⁶ )²

= 40.95 x 10⁻¹⁹ J

Kinetic energy in electron comes from lose of electrical energy equal to

Ve where V is potential difference under which electron is accelerated and e is electronic charge .

V x e = kinetic energy of electron

V x 1.6 x 10⁻¹⁹ = 40.95 x 10⁻¹⁹

V = 25.6 Volt .

6 0
3 years ago
the pygmy shrew has an average mass of 2.0 g if 49 of these shrew are placed on a spring scale with a spring constant of 24 N/m
olga_2 [115]

Answer:

Spring's displacement, x = -0.04 meters.

Explanation:

Let the spring's displacement be x.

Given the following data;

Mass of each shrew, m = 2.0 g to kilograms = 2/1000 = 0.002 kg

Number of shrews, n = 49

Spring constant, k = 24 N/m

We know that acceleration due to gravity, g is equal to 9.8 m/s².

To find the spring's displacement;

At equilibrium position:

Fnet = Felastic + Fg = 0

But, Felastic = -kx

Total mass, Mt = nm

Fg = -Mt = -nmg

-kx -nmg = 0

Rearranging, we have;

kx = -nmg

Making x the subject of formula, we have;

x = \frac {-nmg}{k}

Substituting into the formula, we have;

x = \frac {-49*0.002*9.8}{24}

x = \frac {-0.9604}{24}

x = -0.04 m

Therefore, the spring's displacement is -0.04 meters.

3 0
2 years ago
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