A 2000-turns solenoid has a length of 16cm and a diameter of 3.2cm. (a) Calculat

Question

A 2000-turns solenoid has a length of 16cm and a diameter of 3.2cm.
(a) Calculate its self-inductance.
(b) If the current carried by the solenoid varies with time as I(t) = 200 sin(100t) exp(-t/20) with I in Amps and t in seconds, find the formula for the self-induced electromotive force in the circuit.

(c) If the current carried by the solenoid varies with time as I(t) = 200 sin(100t) exp(-t/20) with I in Amps and t in seconds, find the self-induced electromotive force in the circuit at t=0s, t=3s and t=7s.

PLACE A STEP BY STEP SOLUTION.

SHOW ALL CALCULATIONS.

Explanation / Answer

Part a)

Selfi inductance L=u0xN^2xpixr^2xl

L=4x3.14x10^-7x(2000^2)x3.14x(0.016)^2x0.16

L=0.00064 H

Ans- its self-inductance is 0.00064 H

Part b)

induced emf=-L(dI/dt)

I(t) = 200 sin(100t) exp(-t/20)

dI/dt=200cos(100t)x100xexp(-t/20)+200 sin(100t)x(-1/20)xexp(-t/20)

=20000cos(100t)xexp(-t/20)-100sin(100t)xexp(-t/20)

Part c)

at t=0s ,

emf=20000cos(100t)xexp(-t/20)-100sin(100t)xexp(-t/20)

Put t=0

emf=20000cos(0)xexp(0)-100sin(0)xexp(0

emf=20000V Ans

at t=3s,

emf=20000cos(100x3)xexp(-3/20)-100sin(100x3)xexp(-3/20)

=20000cos(300)x0.86-100x(-0.86)x0.86

emf =8526.04 V Ans

at t=7s,

emf=20000cos(100t)xexp(-t/20)-100sin(100t)xexp(-t/20)

emf=20000cos(700)x0.704-34.2x0.704

emf=13206.79 V Ans

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