The figure below shows a 0.50 cm radius coil with 5 loops and a resistance of 0.

Question

The figure below shows a 0.50 cm radius coil with 5 loops and a resistance of 0.50 ohm placed inside of a 120-turn solenoid with a radius of 1.0 cm and length of 8.0 cm. The graph shows the current in the solenoid as a function of time, with positive current corresponding to clockwise when the solenoid is viewed from the left. Find the current in the coil at t = 0.010 s. The current through a 0.0500 H inductor starts at zero rises linearly to 2 A for 3 s, then drops back linearly to zero over the next 2 seconds. The cycle repeats 2 more times. a. Using Graphical Analysis or Excel, construct a graph of the current over this 15 s period. b. Using Graphical Analysis or Excel, construct a graph of the induced voltage E across the inductor over the same 15 s period. The amplitude of a wave traveling on a string is 1.50 cm. The wave has a frequency of 90.0 Hz and is traveling in the positive x direction with a speed of 16.0 m/s. a. What is the wavelength of the wave? b. Write the position function for this wave. c. Assuming that the phase constant is zero, find the vertical position and the transverse velocity of a particle in the string located at x = 1.5 m at t = 2.00 s.

Explanation / Answer

25. (A) wavelength = speed / frequency

= 16 / 90

= 0.18 m

(B) k = 2 pi / wavelength = 11.25 pi rad / m

w = 2pi f = 180 pi rad/s

y (x ,t) = A cos(kx - wt + phi)

y(x, t) = 1.50 cm cos(11.25 pi x - 180 pi t + phi )

where phi = phase constant

(C) phi= 0 (given)

y (x,t) = 1.50 cm cos(11.25 pi x - 180 pi t)

putting x = 1.5 m and t = 2 s

y = 1.50 cm cos(-343.125 rad)

y = - 1.156 cm

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