QuestionDetails: The voltage source is connected to a load with a resultingcurre

Question

QuestionDetails: The voltage source is connected to a load with a resultingcurrent as shown. Vs(t) = 100cos(377t +130*) V i(t) = 10cos(377t + 10*) A     (i inductor) State the units for each answers a) Calculate the complex power, S, delivered to the load;calculate the real and reactive power for th circuit and statewheter the load is absorbing or delivering power; what are thepower factor and reactive factor? state whether the power factor isleading or legging; Is the load inductive or capacitive?

Explanation / Answer

Given vs (t) = 100 cos(377t +130o) V is (t) = 10 cos(377t +10o)    A Vs = Veff /_o V Effective value of vs(t) is Veff= 100 / 2 = 70.7V Vs = 70.7 /_130oV Is = Ieff /_o V Effective value of vs(t) is Ieff= 10 / 2 = 7.07V Is = 7.07 /_10o V The phase difference between voltage and current is = 130 - 10 = 120o Real Power P = Veff Ieff cos =(70.7)(7.07)(cos120o ) = -250W Reactive Power Q = Veff Ieff sin =(70.7)(7.07)(sin120o ) = 433 VAR Complex Power S = P + jQ S = - 250 + j433 or S = 500 /_- 60o  VA Power factor pf = cos = cos120 pf =-0.5 Reactive factor rf = sin = sin120 rf = 0.866 Power factor is lagging The load is delivering power Effective value of vs(t) is Veff= 100 / 2 = 70.7V Vs = 70.7 /_130oV Is = Ieff /_o V Effective value of vs(t) is Ieff= 10 / 2 = 7.07V Is = 7.07 /_10o V The phase difference between voltage and current is = 130 - 10 = 120o Real Power P = Veff Ieff cos =(70.7)(7.07)(cos120o ) = -250W Reactive Power Is = Ieff /_o V Effective value of vs(t) is Ieff= 10 / 2 = 7.07V Is = 7.07 /_10o V The phase difference between voltage and current is = 130 - 10 = 120o Real Power P = Veff Ieff cos =(70.7)(7.07)(cos120o ) = -250W Reactive Power Effective value of vs(t) is Ieff= 10 / 2 = 7.07V Is = 7.07 /_10o V The phase difference between voltage and current is = 130 - 10 = 120o Real Power P = Veff Ieff cos =(70.7)(7.07)(cos120o ) = -250W Reactive Power Real Power P = Veff Ieff cos =(70.7)(7.07)(cos120o ) = -250W Reactive Power Q = Veff Ieff sin =(70.7)(7.07)(sin120o ) = 433 VAR Complex Power S = P + jQ S = - 250 + j433 or S = 500 /_- 60o  VA Power factor pf = cos = cos120 pf =-0.5 Reactive factor rf = sin = sin120 rf = 0.866 Power factor is lagging The load is delivering power Power factor pf = cos = cos120 pf =-0.5 Reactive factor rf = sin = sin120 rf = 0.866 Power factor is lagging The load is delivering power The load is delivering power

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