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CALC A coil has400 turns and self-inductance 7.50 mH. The current in the coil varies with time according to I =.680×10-3cos[πd/0.0250] (a) What is the maximum emf induced in the coil? (b) What is the maximum average flux through each turn of the coil? (c)At t = 0.0180 s , what is the magnitude of the induced emf?

Short Answer

Expert verified

A) The maximum emf induced in the coil is 0.6406Vb) The maximum average flux through each turn of the coil is role="math" localid="1664181454178" 12.75×10-6c) The magnitude of the induced emf is 0.494V

Step by step solution

01

Concept of the maximum emf induced and the maximum average flux

The maximum emf induced in the coil is given as E=-Ldidtand the maximum average flux through each turn of the coil is given asϕ=LieN

02

Calculate the maximum emf induced in the coil

The coil has 400 turns with self-inductance 7.50 mH and

i=680×10-3cosπd/0.0250.

Substitute the values in the equation E=-Ldidtwe have,

E=-7.50×10-3d680×10-3cosπd/0.0250dt=5100×10-4sin125.6t×125.6Emax=0.6406V

Therefore, the maximum emf induced in the coil is 0.6406V

03

Calculate the maximum average flux through each turn of the coil

The maximum average flux through each turn of the coil is given as ϕ=LieNSubstitute the values

ϕ=7.50×10-3×680×10-3400ϕmax=12.75×10-6

Therefore, the maximum average flux through each turn of the coil is12.75×10-6

04

Calculate the magnitude of the induced emf

From equation E=-Ldidtthe magnitude of the induced emf at t=0.0180sis given as

E=-7.50×10-3×680×10-3-sinπ0.01800.0250×π0.0250=5100×10-6125.6×sin129.6=0.494V

Therefore, the magnitude of the induced emf is0.494V

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