The rotating loop in an AC generator is a square13.0 cm on a side, it is rotated

Question

The rotating loop in an AC generator is a square13.0 cm on a side, it is rotated at 80.0 Hz In a uniform field of 0.800 T. Calculate the following quantities as functions of time t, where t is in seconds. the flux through the loop mT-m^2 the emf induced in the loop V the current induced in the loop for a loop resistance of 1.50 ohm A the power delivered to the loop W the torque that must be exerted to rotate the loop mN-m A conducting rod of length C moves with velocity parallel to a long wire carrying a steady current f.

Explanation / Answer

Here ,

d = 0.13 m

f = 80 Hz

B = 0.8 T

a) flux through the loop = 0.13^2 * 0.80 * cos(2pi * f * t)

flux through the loop = 0.01352 * cos(502.6 * t)

flux through the loop = 13.52 * cos(502.6 * t)

b)

for the emf induced

emf induced = 0.01352 * sin(502.6 * t) * 80 * 2pi

emf induced = 6.79 * sin(502.6 * t)

c)

for the current

current in the loop = emf/R

current in the loop = 6.79 * sin(502.6 * t)/1.50

current in the loop = 4.53 * sin(502.6 * t)

d)

power delivered to the loop = V * I

power delivered to the loop = 6.79 * sin(502.6 * t) * 4.53 * sin(502.6 * t)

power delivered to the loop = 30.8 * sin^2(502.6 * t)

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