Final answer:
The induced emf in a generator coil can be calculated by applying Faraday's Law, using the coil's number of turns, the area of the coil, magnetic field strength, and angular velocity. For the peak emf, we consider the sine function to be at its maximum.
Step-by-step explanation:
To determine the electromotive force (emf) induced in the generator coil, one applies Faraday's Law of electromagnetic induction. Given that the coil has 200 turns and rotates at 3450 revolutions per minute (rpm) in a magnetic field of 0.65 teslas (T), we can use these values to calculate the induced emf.
The formula for induced emf (E) in a rotating coil is given by:
E = NABωsin(ωt)
where:
- N is the number of turns in the coil,
- A is the area of the coil,
- B is the magnetic field strength,
- ω is the angular velocity, and
- t is the time.
Converting the diameter to radius and revolutions per minute to radians per second is necessary:
Radius (r) = Diameter / 2 = 0.11 m / 2
Angular velocity (ω) = 3450 rpm × (2π radians/revolution) × (1 minute/60 seconds)
Since we want the peak voltage, we look at the case where sin(ωt) = 1, which happens when the coil is perpendicular to the magnetic field lines:
Peak emf (E_peak) = NABω
Substituting the values:
Peak emf (E_peak) = 200 × (π × (0.11/2)^2) × 0.65 × 3450 × (2π/60)
After calculating the above expression, we obtain the value of the peak emf induced in the coil.