In the figure below, the rod moves with a speed of 1.9 m/s, is 29.5 cm long, and
ID: 1552185 • Letter: I
Question
In the figure below, the rod moves with a speed of 1.9 m/s, is 29.5 cm long, and has a resistance of 2.5 ohm. The magnetic field is 0.70 T, and the resistance of the U-shaped conductor is 25.0 ohm at a given instant. (a) Calculate the induced emf. V (b) Calculate the current in the U-shaped conductor. A (c) Calculate the external force needed to keep the rod's velocity constant at that instant. N (to the right) A 300 loop circular armature coil with a diameter of 5.0 cm rotates at 120 rev/s in a uniform magnetic field of strength 0.55 T. (a) What is the rms voltage output of the generator? V (b) What would you do to the rotation frequency in order to double the rms voltage output? half the rotation frequency do nothing double the rotation frequency Neon signs require 18 kV for their operation. To operate from a 120 V line, what must be the ratio of secondary to primary turns of the transformer? What would the voltage output be if the transformer were connected backward? V How many turns of wire would be required to make a 100 mH inductance out of a 30.0 cm long air-filled coil with a diameter of 5.2 cm? turnsExplanation / Answer
Given
v = 1.9 m/s, l = 0.295 m, B = 0.70 T
resistance of the rod is r = 2.5 ohm
u shaped conductor resistance r = 25 ohm
a) induced emf e = B*vl sin theta = 0.7*1.9*0.295 sin90 V = 0.39235 V
b) induce current in the u shaped conductor is i= e/(r+R) = 0.39235/(2.5+25) A = 0.01427 A
c) Force need is F = Bil sin theta
i = e/(r+R)
F = B^2*l^2*v/(r+R)
F = 0.7^2*0.295^2*0.39235 /(27.5) N = 0.60838861 mN
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Given
N = 300 circular armature coil diameterd = 5 cm, radius r = 0.025 m,
w = 120 rev/s , B= 0.55 T
induced emf = - d phi/dt
phi is magnetic flux, = B*A*N cos theta
e = B*A*N*W sin (Wt)
A = are of the circle = pi*r^2 = 3.14*0.025^2 m2 = 0.0019635 m2
e = 0.55*0.0019635*300*120*2pi/60 sin(4pit)
maximum emf is if sin (4pit)= 1
e = 4.07122 V
the rms voltage out put of the generator is Vrms = 0.707*Vmax = 0.707*4.07122 V = 2.87835254 V
b)
in order to double the voltage out put , doubling the rotation frequency of generatot