If the speed of a universal motor in AC operation is $$N_{AC}$$ and in DC operation is $$N_{DC}$$, (and I = current, V = supply voltage, r = resistance, X = reactance, $$\cos \phi$$ = power factor) then the speed ratio

A

$$\frac{N_{AC}}{N_{DC}} = \frac{\cos \phi - \frac{IX}{V}}{1 - \frac{Ir}{V}}$$

B

$$\frac{N_{AC}}{N_{DC}} = \frac{1 - \frac{Ir}{V}}{\cos \phi - \frac{IX}{V}}$$

C

$$\frac{N_{AC}}{N_{DC}} = \frac{1 - \frac{Ir}{V}}{\cos \phi - \frac{Ir}{V}}$$

D

$$\frac{N_{AC}}{N_{DC}} = \frac{\cos \phi - \frac{Ir}{V}}{1 - \frac{Ir}{V}}$$