Please show the work and explain. Thanks. :D As you know, if you put two DC volt

Question

Please show the work and explain. Thanks. :D

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 V0 middot sin(t) and the other looks like V0 middot sin(omega t + delta). delta 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 = 18 V, omega = 185 rad/s, and delta = 0.55 rad. You'll probably need to work from the definition of root-mean-square. You can get a short, tidy algebraic answer by using trig identities, or you may use a computer to grind out any difficult integrals. Whatever you prefer.

Explanation / Answer

you only need to know the final amplitude of the wave, which you can get by vector addition. having the amplitude, then amp/sqrt(2) is your rms voltage.

so to add two vectors of same length (vo) under an angle of 0.6 rad, gives you a resultant vector length of v0 * sqrt( [1 (plus) cos(0.6]^2 (plus) [sin(0.6)]^2) = v0 * 1.91

so the rms = 26V * 1.91/sqrt(2) = 35.1 V

(proof? work it out for a phase diff of pi, you should get zero!)

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