Question

a)The voltage across two series connected

circuit elements ate V.: t00 sinw/ V and

Vr= 50 sin(wr - 30') v. If the circuit

ctrrrent is {4 + iZ)A. Find the complex power

in the circuit.

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Answer 1

Answer:

Express the given voltages in POLAR FORM and then add them accordingly:

V1 = 50(-30) volts => Assuming v1 = 50sin(377t - 30 degrees)

V2 = 20(45) volts

V3 = 50(150) volts

=> a basic cosine wave LEADS a sine wave by 90 degrees => hence sin(theta + 90 degrees) = cos(theta). Consequently, 50cos(377t + 60 degrees) = 50sin(377t + 150 degrees)

Adding the above POLAR FORM numbers gives 20(45) volts.

In terms of time the resultant voltage is therefore given by v1 + v2 + v3 = 20sin(377t + 45 degrees) volts.

RMS value = 20*0.707 = 14.14V

frequency = 377 / (2 * pi) = 60Hz