When its coil rotates at a frequency of 262 Hz, a certain generator has a peak emf of 79 V. (a) What is the peak emf of the generator when its coil rotates at a frequency of 46 Hz? (b) Determine the frequency of the coil's rotation when the peak emf of the generator is 186 V?

To find the peak emf of the generator at different frequencies, we can set up a proportion using the known values. When the frequency is 46 Hz, the peak emf is approximately 13.91 V. When the peak emf is 186 V, the frequency is approximately 615.95 Hz.

Explanation:

To find the peak emf of the generator when its coil rotates at a different frequency, we can use the relation between frequency and peak emf. The peak emf of a generator is directly proportional to its frequency. So, we can set up a proportion to solve for the peak emf when the frequency is 46 Hz:

79 V / 262 Hz = X V / 46 Hz

Simplifying the proportion, we get X = (79 V / 262 Hz) * 46 Hz ≈ 13.91 V.

For part (b), we can use the same proportion to find the frequency when the peak emf is 186 V:

79 V / 262 Hz = 186 V / X Hz

Simplifying the proportion, we get X = (262 Hz / 79 V) * 186 V ≈ 615.95 Hz.