A 20 turn square coil has an area 19.0 cm 2 and is rotated with an angular speed

Question

A 20 turn square coil has an area 19.0 cm2 and is rotated with an angular speed of 170.0 rad/s in a uniform 0.30 T magnetic field. The axis of the coil is perpendicular to the field at all times.

What is the frequency of the sinusoidal voltage induced across its ends? 27.1 Hz

What is the peak voltage induced across the ends of the coil? 1.94 V

What is the average power dissipated in the resistor? 0.0376 W

What is the flux through the coil when the plane of the coil is inclined at 18.0° to the magnetic field?
3.52 mWb

If the coil forms a closed circuit with a series resistance of 50.0 , what is the instantaneous power being dissipated in the resistor when the plane of the coil makes an angle of 18.0° with the magnetic field?

I do not how to do the last question.

I tried

V = N*B*A*w*sin(90 - 18.0) V = 20 * 0.30 * 19.0 * 10^-4 * 170.0 * sin(72)

P=V^2/R=0.0679 W(Incorrect)

V = BANsin = BANsin() = 0.30*19*10^-4 *20*170 * sin( 18) = 0.598875 V

P =V^2 /R = 0.598875^2 / 50 = 0.00717302531 W(Incorrect)

I think the answer will be either 0.0679 W or 0.00717302531 W, but it is not.

What is the definition of instantaneous power? How to slove the last question?

Explanation / Answer

n = 20
w = 170 /s
B = 0.3 T
flux = nBAcos(wt)
EMF = d(flux)/dt = nBAwsin(wt)

Instantaneous power = V^2/R = (20*0.3*0.0019*170sin(18))^2/50 = 0.007173 W

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