The eddy current losses in a synchronous motor are 100 watts at 100 Hz. Find the frequency, if the losses are to be reduced to 25 W?

Correct option is A

​$$\text{Eddy current loss } (P_e) = K_e f^2 B_{\text{max}}^2 t^2 \\\text{ where }\\ K_e = \text{Eddy current loss constant, } f = \text{Frequency, } B_{\text{max}} = \text{maximum flux density, } t = \text{thickness.}\\\text{Calculation:}\\B_{\text{max}} = \text{constant}\\P_e \propto f^2\\\frac{P_{c2}}{P_{e1}} = \frac{f_2^2}{f_1^2}\\f_2^2 = f_1^2 \times \frac{P_{c2}}{P_{c1}} = \frac{100^2 \times 25}{100} = 2500\\f_2 = 50 \, \text{Hz}$$​​