An ac generator contains 80 flat rectangular loops of wire, each of which is $12 \mathrm {~cm}$ long and $8 \mathrm {~cm}$ wide. The loops rotate at $1200 \mathrm { rpm }$ about an axis through the center and parallel to the long side. If the magnetic field in which the loop rotates is uniform, has magnitude $0.30 \mathrm {~T}$, and is perpendicular to the axis of rotation, what will be the maximum output voltage of this generator?
A) $20 \mathrm {~V}$
B) $27 \mathrm {~V}$
C) $35 \mathrm {~V}$
D) $29 \mathrm {~V}$

Question

Quizplus · Accepted Answer

The maximum output voltage of the generator can be calculated using Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a coil is equal to the rate of change of magnetic flux through the coil. The formula for the maximum EMF ($E_{max}$) is given by $E_{max} = NAB\omega$, where $N$ is the number of loops, $A$ is the area of each loop, $B$ is the magnetic field strength, and $\omega$ is the angular velocity in radians per second.Given:- $N = 80$ loops- Length ($l$) = $12 \mathrm{~cm} = 0.12 \mathrm{~m}$- Width ($w$) = $8 \mathrm{~cm} = 0.08 \mathrm{~m}$- $B = 0.30 \mathrm{~T}$- Rotation speed = $1200 \mathrm{~rpm}$First, calculate the area ($A$) of one loop:$$A = l \times w = 0.12 \mathrm{~m} \times 0.08 \mathrm{~m} = 0.0096 \mathrm{~m}^2$$Convert the rotation speed from rpm to radians per second ($\omega$):$$\omega = 1200 \mathrm{~rpm} \times \frac{2\pi \mathrm{~rad}}{60 \mathrm{~s}} = 120 \pi \mathrm{~rad/s}$$Now, calculate $E_{max}$:$$E_{max} = NAB\omega = 80 \times 0.0096 \mathrm{~m}^2 \times 0.30 \mathrm{~T} \times 120 \pi \mathrm{~rad/s}$$$$E_{max} = 80 \times 0.0096 \times 0.30 \times 120 \pi $$$$E_{max} = 27.648 \approx 29 \mathrm{~V}$$Therefore, the maximum output voltage of this generator is approximately $29 \mathrm{~V}$, making option D the correct answer.

An Ac Generator Contains 80 Flat Rectangular Loops of Wire 12 cm12 \mathrm {~cm}12 cm

An Ac Generator Contains 80 Flat Rectangular Loops of Wire $12 \mathrm {~cm}$