Final answer:
To calculate the peak voltage of a generator, convert rpm to radians per second, find the area of the coil, and use Faraday's law, taking into account the number of turns, area, magnetic field strength, and angular velocity.
Step-by-step explanation:
To calculate the peak voltage of a generator, we use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a coil is proportional to the rate of change of the magnetic flux through the coil. The equation for the induced emf (ε) is ε = 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, and ω is the angular velocity of the coil. The peak voltage is reached when sin(ωt) = 1.
First, we convert the coil's diameter to radius (r) by dividing by 2, which gives us a radius of 0.11 m / 2 = 0.055 m.
Next, we calculate the coil's area (A = πr²) to be A = π(0.055 m)².
The angular velocity (ω) in radians per second is obtained by converting the rotation speed from rpm to rad/s by multiplying by 2π/60. Therefore, ω = 3450 rpm * 2π/60.
With all values in hand, we calculate the peak voltage using the formula.
Remember that the peak voltage is the maximum voltage the generator can produce, and this happens when sin(ωt) equals 1, which corresponds to when the coil is perpendicular to the magnetic field lines at a certain instant during the rotation.