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22 January, 15:20

A tightly wound solenoid of 1600 turns, cross-sectional area of 6.00 cm2, and length of 20.0 cm carries a current of 2.80 A. (a) What is its inductance? (b) If the cross-sectional area is doubled, does anything happen to the value of the inductance? Explain your answer.

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  1. 22 January, 15:46
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    (a) 9.65 mH

    (b) doubled

    Explanation:

    A = 6 cm^2 = 6 x 10^-4 m^2, l = 20 cm = 0.2 m, i = 2.8 A, N = 1600

    (a) The formula for the self inductance of a solenoid is given by

    L = μ0 N^2 A / l

    L = 4 x 3.14 x 10^-7 x 1600 x 1600 x 6 x 10^-4 / 0.2

    L = 9.65 x 10^-3 H

    L = 9.65 mH

    (b) As we observe that the inductance is proportional to the area so if the area is doubled, then inductance is also doubled.
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