A) We differentiate the expression for velocity to obtain an expression for acceleration:
v(t) = 1 - sin(2πt)
dv/dt = -2πcos(2πt)
a = -2πcos(2πt)
b) Any value of t can be plugged in as long as it is greater than or equal to 0.
c) we integrate the expression of velocity to find an expression for displacement:
∫v(t) dt = ∫ 1 - sin(2πt) dt
x(t) = t + cos(2πt)/2π + c
x(0) = 0
0 = = + cos(0)/2π + c
c = -1/2π
x(t) = t + cos(2πt)/2π -1/2π
Answer:
(a): emf =
(b): Amplitude of alternating voltage = 20.942 Volts.
Explanation:
<u>Given:</u>
- Area of the coil = A.
- Number of turns of coil = N.
- Magnetic field = B
- Rotation frequency = f.
(a):
The magnetic flux through the coil is given by
where,
= area vector of the coil directed along the normal to the plane of the coil.
= angle between and .
Assuming, the direction of magnetic field is along the normal to the plane of the coil initially.
At any time t, the angle which magnetic field makes with the normal to the plane of the coil is
Therefore, the magnetic flux linked with the coil at any time t is given by
According to Faraday's law of electromagnetic induction, the emf induced in the coil is given by
(b):
The amplitude of the alternating voltage is the maximum value of the emf and emf is maximum when
Therefore, the amplitude of the alternating voltage is given by
We have,
Putting all these values,
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