As you know, if you put two DC voltage sources in series, you can provide a larg

Question

As you know, if you put two DC voltage sources in series, you can provide a larger voltage to an application. For example, two 1.5V AA batteries in series provides 3V. You can do the same thing with AC voltage, though the situation is more complicated. Suppose you have two AC voltage sources that have the same amplitude and frequency, but are out of phase with one another. In mathematical terms, one of the voltage functions looks like V0sin(t) and the other looks like V0sin(t+). is referred to as a phase offset and is in radians. If you add those sources together, what's the rms voltage of the resulting signal? Let V0 = 13 V, = 264 rad/s, and = 0.70 rad.

Explanation / Answer

u can treat them as 2 vectors with magnitude V o and the angle between them as delta

which give the magnitude =2Vcos delta/2 = 25.99 v

rms = max/ 1.4.14

rms = 18.38 volts

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