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I have the question " The instantaneous values of two alternating currents are given by i1 = 20sinwt amperes and i2 = 10sin(wt + pi/3) amperes. By plotting i1 and i2 on the same axes, using the same scale, over one cycle, and adding ordinates at intervals, obtain a sinusoidal expression for i1 + i2."

The graph for the question is:

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The answer for the sinusoidal expression is:

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I understand everything except for the 19 degrees. The solutions say that the resultant waveform leads the curve i1 = 20sinwt by 19 degrees which is 0.332 rads, however I do not understand where the 19 degrees came from.

1 Answers 1

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Let the resultant equation be $26.5\sin (wt+a) $ now at any time $t $ resultant displacements of two waves and this new wave should be equal as both are equal. Now for simplifications put $t=0$ for first two currents the resultant is $0+8.66$ this should be equal to $26.5 \sin (0+a) $ thus $8.66=26.5\sin (a) $ which gives $a\approx 19^\circ. $