ANSWER: 0.682 A I leads V by 90 degrees 11. (20 pts) A long straight solenoid th

Question

ANSWER: 0.682 A

I leads V by 90 degrees

11. (20 pts) A long straight solenoid that has a length of 0.500 m, radius of 7.50 cm, and 1500 turns of wire is shown in side view (left) and end-on view (right) below. The solenoid is connected to an AC voltage source and a capacitor as shown. The capacitor has a capacitance of 50.0 F, and the AC voltage source has an output as a function of time given by v(t) = V cos(wt) where positive v(t) is indicated by the + and - signs next to the voltage source. A current i(t) flows in the circuit due to the AC voltage source, where positive i(t) i indicated by the direction of the arrows in the figure (clockwise as seen in the end-on view). (Negative v(t) and negative i(t) are in the opposite directions.) For V 10.0 V, and w 380 rad/s, (a) What is the maximum value of i(t) in the solenoid circuit? (b) What is the phase difference between the current in the circuit and the AC voltage source? Which leads?

Explanation / Answer

a)given

l = 0.5 m
r = 7.5 cm = 0.075 m

Area , A = pi*r^2 = pi*0.075^2 = 0.01767 m^2

N = 1500 turns

slef inductance of solenoid, L = mue*N^2*A/l

= 4*pi*10^-7*(1500)^2*0.01767/0.5

= 0.100 H

inductive recatnce, XL = w*L

= 380*0.1

= 38 ohms

capacitive recatnce, Xc = 1/(w*C)

= 1/(380*50*10^-6)

= 52.6 ohms

impdance of the ckt, z = Xc - XL

= 52.6 - 38

= 14.6 ohms

Imax = Vmax/z

= 10/14.6

= 0.685 A

b)
phase angle,
theta = tan^-1( (XL - XC)/R)

= tan^-1(infinite) (since R = 0)

= 90 degrees

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