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3 years ago

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A technician wraps wire around a tube of length 38 cm having a diameter of 8.3 cm. When the windings are evenly spread over the

full length of the tube, the result is a solenoid containing 555 turns of wire.(a) Find the inductance of this solenoid.

1 answer:

seropon [69]3 years ago

7 0

Answer:

The inductance of this solenoid is 5.51 mH.

Explanation:

Given that,

length of the tube, l = 38 cm = 0.38 m

Diameter of the tube, d = 8.3 cm

Radius of the tube, r = 4.15 cm

The number of turns, N = 555

We need to find the inductance of this solenoid. It is given by the formula as :

$L=\dfrac{\mu N^2A}{l}\\\\L=\dfrac{4\pi \times 10^{-7}\times 555^2\times \pi \times (4.15\times 10^{-2})^2}{0.38}\\\\L=0.00551\ H\\\\L=5.51\ mH$

So, the inductance of this solenoid is 5.51 mH. Hence, this is the required solution.

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$\tau = T r$

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$Tr = I \alpha$

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$(mg - ma ) r = I\ r \alpha$

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$a = r\alpha$

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$mgr = I\alpha + m(r\alpha ) r$

$mgr = \alpha [ I + mr^2]$

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$\alpha = \frac{mgr}{I -mr ^2}$

Substituting values

$\alpha = \frac{61.2 * 1.5 * 9.8}{15.975 + (61.2 ) * (1.5)^2}$

$\alpha =5.854 rad /s^2$

Now substituting into the equation above to obtain the acceleration

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$v = \frac{8}{0.9545}$

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$w = 5.59 rad/s$

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$x = \frac{5.59 * 0.159155}{1}$

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Now z is mathematically obtained as

$z = \frac{ 1}{60}$

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Therefore

$w = \frac{0.8892}{0.01667}$

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