The maximum induced emf in a generator whose coils are rotating at 240 rpm is 35 V. If, instead, it is desired to generate a maximum emf of 45 V but with half the magnetic field, what rotation rate must be used?
A) 380 rpm
B) 190 rpm
C) 310 rpm
D) 165 rpm
E) 620 rpm

Question

Quizplus · Accepted Answer

The induced emf ($E$) in a generator is directly proportional to the magnetic field strength ($B$) and the rotation rate ($n$). Mathematically, this can be expressed as $E \propto Bn$. Given that the maximum emf is to be increased from 35 V to 45 V (a factor of $45/35 = 1.29$) while the magnetic field is halved, the rotation rate must be increased by a factor of $2 \times 1.29 = 2.58$ to compensate. Therefore, the new rotation rate is $240 \, \text{rpm} \times 2.58 = 619.2 \, \text{rpm}$, which rounds to 620 rpm, option E.

The Maximum Induced Emf in a Generator Whose Coils Are