14. (Faraday\'s law of induction) A 0.1 m long solenoid has a radius of 0.05 m a

Question

14. (Faraday's law of induction) A 0.1 m long solenoid has a radius of 0.05 m and 1.5x10* turns The current in the solenoid changes at a rate of 9 A/s. A conducting loop of radius 0.02 m is placed at the center of the solenoid with its axis the same as that of the solenoid. (14a) What is the induced emf in the loop? (14b) What is the self-induced emf in the solenoid due to the changing current? 15. (RLC Series Circuit) Suppose an AC generator with Vt)-(i50 V) sin (100 t) is connected to a series RLC circuit with R-40 ?, L-80 mH, and C-50.0 uF, as shown in the Figure. VO-Vo sinot (15a) Find the inductive reactance, capacitive reactance and the impedance of the circuit (15b) Find the corresponding maximum current amplitude lo (15c) Find the phase angle between the voltage and the current in an AC circuit

Explanation / Answer

from the given data

Vmax = 150 V
w = 100 rad/s

a) inductive reactance, XL = w*L

= 100*80*10^-3

= 8.0 ohms <<<<<<-------------Answer

capacitive reactnace, XC = 1/(w*c)

= 1/(100*50*10^-6)

= 200 ohms <<<<<<-------------Answer

impedance, z = sqrt(R^2 + (XL - XC)^2)

= sqrt(40^2 + (8 - 200)^2)

= 196 ohms <<<<<<-------------Answer

b) Io = Vmax/z

= 150/196

= 0.765 A <<<<<<-------------Answer

c) phase angle, phi = tan^-1( (XL - XC)/R)

= tan^-1( (8 - 200)/40)

= 78.2 degrees <<<<<<-------------Answer

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