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2 years ago

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(a) Calculate the self-inductance of a 42.2 cm long, 10.0 cm diameter solenoid having 1000 loops. (b) How fast can it be turned

off if the induced emf cannot exceed 3.00 V and a current of 18.6 A flows through this inductor?

1 answer:

kaheart [24]2 years ago

6 0

Answer:

self-inductance is 23.4 mH

0.145 seconds it be turned off

Explanation:

given data

length L = 42.2 cm

diameter d = 10 cm

no of loop N = 1000 loops

induced emf = 3 V

current I = 18.6 A

to find out

self-inductance and How fast it turned off emf

solution

we apply here formula of self-inductance that is

self-inductance = u×N²×A / L .......................1

put here value

self-inductance = 4π×1000²×(π×r² / 0.422)

self-inductance = 4π×1000²×(π×0.05² / 0.422)

self-inductance = 0.0234 H

so self-inductance is 23.4 mH

and

we know emf = Ldi /dt

so time = 0.0234 × 18.6

time = 0.145 seconds

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The initial momentum will be:

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$m_{total} = m_{Al} + m_{Jo} = 195 \ kg$ .

so:

$m_{Jo} = 195 \ kg - m_{Al}$ .

$m_{Al} \ v_{Al_f} + (195 \ kg - m_{Al}) \ v_{Jo_f} = 0$

$m_{Al} \ v_{Al_f} - m_{Al} \ v_{Jo_f}= - 195 \ kg \ v_{Jo_f}$

$m_{Al} \ (v_{Al_f} - v_{Jo_f})= - 195 \ kg \ v_{Jo_f}$

$m_{Al} = \frac{ - 195 \ kg \ v_{Jo_f} } { v_{Al_f} - v_{Jo_f} }$

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Now, we can use the values:

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where the minus sign appears as they are moving at opposite directions

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