Given the following voltage and current on the load, find the power factor, average power, reactive power, complex power, and apparent power. Also, find the equivalent impedance, equivalent resistance, and equivalent inductance of the load. Draw the phasors for P, Q, and S.
The voltage and current are peak values. $$v ( t ) = 150 \cos \left( 2 \pi 60 t + 120 ^ { \circ } \right) \mathrm { V } , i ( t ) = 10 \cos \left( 2 \pi 60 t + 85 ^ { \circ } \right) \mathrm { A }$$

Question

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The Answer is The difference in phase angle is

heta = heta _ { \mathrm { v } } - heta _ { \mathrm { i } } = 120 ^ { \circ } - 85 ^ { \circ } = 35 ^ { \circ }

The power factor is given by

ext { pf } = \cos ( heta ) = \cos \left( 35 ^ { \circ } ight) = 0.819152

The average power is

P = \frac { V _ { m } I _ { m } } { 2 } p f = \frac { 150 imes 10 } { 2 } imes 0.819152 = 614.364 \mathrm {~W}

The reactive power is

Q = \frac { V _ { m } I _ { m } } { 2 } \sin ( heta ) = \frac { 150 imes 10 } { 2 } \sin \left( 35 ^ { \circ } ight) = 430.1823 \mathrm { VAR }

The complex power is given by

\mathbf { S } = \mathrm { P } + \mathrm { jQ } = 614.364 + \mathrm { j } 430.1823 = 750 \angle 35 ^ { \circ } \mathrm { VA }

The apparent power is given by

| \mathrm { S } | = 750 \mathrm { VA }

$The difference in phase angle is heta = heta _ { \mathrm { v } } - heta _ { \mathrm { i } } = 120 ^ { \circ } - 85 ^ { \circ } = 35 ^ { \circ } The power factor is given by ext { pf } = \cos ( heta ) = \cos \left( 35 ^ { \circ } ight) = 0.819152 The average power is P = \frac { V _ { m } I _ { m } } { 2 } p f = \frac { 150 imes 10 } { 2 } imes 0.819152 = 614.364 \mathrm {~W} The reactive power is Q = \frac { V _ { m } I _ { m } } { 2 } \sin ( heta ) = \frac { 150 imes 10 } { 2 } \sin \left( 35 ^ { \circ } ight) = 430.1823 \mathrm { VAR } The complex power is given by \mathbf { S } = \mathrm { P } + \mathrm { jQ } = 614.364 + \mathrm { j } 430.1823 = 750 \angle 35 ^ { \circ } \mathrm { VA } The apparent power is given by | \mathrm { S } | = 750 \mathrm { VA } \begin{array} { l } \mathbf { Z } = \mathbf { V } / \mathbf { I } = 12.2873 + \mathrm { j } 8.6036 \Omega \ \mathrm { R } = 12.2873 \Omega \ \mathrm { X } = 8.6036 \Omega \ \mathrm { L } = \mathrm { X } / \omega = \mathrm { X } / ( 2 \pi \mathrm { f } ) = 22.8219 \mathrm { mH } \end{array}$

\begin{array} { l } \mathbf { Z } = \mathbf { V } / \mathbf { I } = 12.2873 + \mathrm { j } 8.6036 \Omega \\mathrm { R } = 12.2873 \Omega \\mathrm { X } = 8.6036 \Omega \\mathrm { L } = \mathrm { X } / \omega = \mathrm { X } / ( 2 \pi \mathrm { f } ) = 22.8219 \mathrm { mH }\end{array}

Given the Following Voltage and Current on the Load, Find