Given the Following Voltage and Current on the Load, Find$$v ( t ) = 150 \cos \left( 2 \pi 60 t + 120 ^ { \circ } \right) \mathrm { V } , i ( t ) = 10 \cos \left( 2 \pi 60 t + 85 ^ { \circ } \right) \mathrm { A }$$

Question

Examlex · Accepted Answer

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

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