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Addition of sinusoidal waves

Please see the 2 problems attached

Q4.Two alternating currents i1 and i2 flow in a circuit node. The output current i is given by i1 + i2.

If i1 = 5sin( 50t + /3 ) and i2 = 6cos50t

Calculate the amplitude of i and the first time that it occurs.

Q5. The instantaneous power p, in an electric circuit, is given by p = iv, where v is voltage and i is current.
Calculate the maximum value of power in the circuit if:

v = 0.02 sin(100t)volts, and i = 0.6 sin(100t + /4)amps

Also calculate the first time that the power reaches a maximum value.


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Solution Summary

When two sinusoidal waves with the same frequency are added the resultant signal is a sinusoidal wave as well.
The solution shows how to derive the expression for the resultant signal and how to use it to find what is the signal's new amplitude and when it achieves maxima.
then we see how to multiply two signals to calculate the power using Euler's identity.