A generator is designed to produce a maximum emf of 170 V while rotating at 3200 rpm. The coils of the generator are circular with diameter 7.50 cm. Assuming the magnetic field in the generator is 0.0750 T, what is the number of loops needed in the generator coil?
A) 160
B) 1530
C) 6120
D) 4810
E) 25

Question

Quizplus · Accepted Answer

The maximum emf of a generator is given by $\mathcal{E}_{max} = NBA\omega$, where $N$ is the number of loops, $B$ is the magnetic field, $A$ is the area of the loop, and $\omega$ is the angular frequency. Solving for $N$ we get $N=\frac{\mathcal{E}_{max}}{BA\omega}$. Since the diameter is given, we need to find the radius and then find the area of the circular coil. The radius is half the diameter, so $r=3.75	ext{ cm} = 0.0375 	ext{ m}$. The area of the circular coil is $A=\pi r^2 = 1.767 	imes 10^{-3} 	ext{ m}^2$. Plugging in the given values we get $N=\frac{(170	ext{ V})}{(0.0750	ext{ T})(1.767 	imes 10^{-3} 	ext{ m}^2)(2\pi \cdot 3200 	ext{ rpm}/60)} \approx 1530$, which is closest to answer choice B.

A Generator Is Designed to Produce a Maximum Emf of 170