Cosφ is the power factor. It’s the ratio of real power to apparent power (cosφ = P/S) and also the cosine of the phase angle between voltage and current. This tells you how effectively the supplied power is doing useful work. If the voltage and current are in phase (φ = 0), cosφ = 1, meaning all the power is real power. As φ grows due to inductive or capacitive effects, cosφ drops, and some power becomes reactive rather than doing useful work. It’s not a measure of efficiency, nor the phase angle itself (that would be φ), nor the impedance value.

For a sine wave, the RMS value is the peak value divided by the square root of 2. If the instantaneous voltage is v(t) = Vp sin(ωt), squaring gives v(t)^2 = Vp^2 sin^2(ωt). The average value of sin^2 over a full cycle is 1/2, so the average of v(t)^2 is Vp^2/2. Taking the square root yields Vrms = sqrt(Vp^2/2) = Vp / √2. This means the RMS voltage is about 0.707 times the peak voltage. So the correct relationship is Vrms = Vpeak / √2. The other options don’t fit because they either equate RMS to the peak (which ignores the averaging of the squared value), multiply by √2 (which would give a value larger than the peak), or divide by 2 (which is not the proper factor after taking the square root).

In a series circuit with a resistor, inductor, and capacitor, resonance occurs when the inductive and capacitive reactances balance each other so their net reactive effect is zero. The total impedance is Z = R + j(X_L − X_C). At resonance, X_L = X_C, so the imaginary part is zero and Z reduces to R. This means the circuit behaves as a purely resistive load at the resonance frequency, with the current determined by the resistance and no net reactive energy storage over a cycle. If X_L were greater than X_C, the circuit would appear inductive; if X_L were less than X_C, it would appear capacitive. In either case, there would be a nonzero reactive component, not the purely resistive result seen at resonance. The impedance being infinite would not occur in a series R-L-C circuit with a resistor; the current would still flow limited by the resistance.

In a 9-lead motor, there are three windings, each with two ends and a center tap. The two ends of the same winding show the full winding resistance between them, while each end to its center tap reads about half that resistance, and the center taps themselves are separate leads. Typically the windings are paired as follows: ends T1 and T4 with center tap T7 form one winding; ends T2 and T5 with center tap T8 form another; ends T3 and T6 with center tap T9 form the third. So the two ends of the same coil are T1 and T4.