The voltage v(t) = 141.4 cos (ωt) is applied to a load consisting of a 10Ω resistor in parallel with an inductive reactance XL=ωL = 3.77Ω. Calculate the instantaneous power absorbed by the resistor and by the inductor. Also calculate the real and reactive power absorbed by the load, and the power factor. Draw all the voltage, current and power waveforms, also the draw the circuit and phasor diagrams.

A) P(t) = 2651.25 [ 1 - cos2wt ] W

B)  Real power = 999.79 watts

    Reactive power = 2652.86 VA

c) power factor = 0.3526

Explanation:

Given data:

V(t) = 141.4 cos (ωt)

R(t) = 10 Ω

Inductive reactance XL = ωL = 3.77 Ω

Ir(t) = V(t) / R(t) = 14.14

A) Calculate the instantaneous power absorbed by the resistor and by inductor

By resistor :

Pr(t) = V(t) * Ir(t) = 141.4 * 14.14 = 1999.396

      hence Pr  = 999.698 (cos2ωt + 1) w

By Inductor :

Pl(t) = V(t) I'L(t) = 141.4 cosωt * 37.5 cos(ωt - 90)  

                        =  5302.5

Hence Pl(t) = 5302.5   w  =  2651.25 [ 1 - cos2wt ] W

B) calculate the real and reactive power

First we have to determine the power factor

Given that : V(t) = 141.4 cosωt  v ,   Ir(t) = 14.14 cosωt A

IL(t) = 37.5 cos (ωt - 90° )

The phasor representation of the above is :

V = = 141.4 ∠0° ,  Ir = 10 ∠ 0° , IL = 37. 5 ∠ -90°

Total load current = Ir + IL = 28.35 ∠ -69.35°

power factor = cos -69.35° = 0.3526

Next we will determine the Real and reactive power using the relation below

S = VI = 100 ∠ 0°  * 28.35 ∠ -69.35°

         = 2835 ∠ 69.35°

S = P + jQ = 999.79 + 2652.85 j

Real power  = 999.79 watts

Reactive power = 2652.85 VA

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