Given the Following Voltage and Current on the Load, Find$$v ( t ) = 140 \cos \left( 2 \pi 60 t + 30 ^ { \circ } \right) \mathrm { V } , i ( t ) = 12 \cos \left( 2 \pi 60 t + 55 ^ { \circ } \right) \mathrm { A }$$

Question

Examlex · Accepted Answer

The Answer is The difference in phase angle is

heta = heta _ { \mathrm { v } } - heta _ { \mathrm { i } } = 30 ^ { \circ } - 55 ^ { \circ } = - 25 ^ { \circ }

The power factor is given by

\mathrm { pf } = \cos ( heta ) = \cos \left( - 25 ^ { \circ } ight) = 0.906308

The average power is

P = \frac { V _ { m } I _ { m } } { 2 } p f = 761.29854 \mathrm {~W}

The reactive power is

Q = \frac { V _ { m } I _ { m } } { 2 } \sin ( heta ) = - 354.99934 \mathrm { VAR }

The complex power is given by

\mathbf { S } = \mathrm { P } + \mathrm { jQ } = 761.29854 - \mathrm { j } 354.99934 = 840 \angle - 25 ^ { \circ } \mathrm { VA }

The apparent power is given by

| \mathrm { S } | = 840 \mathrm { VA }

$The difference in phase angle is heta = heta _ { \mathrm { v } } - heta _ { \mathrm { i } } = 30 ^ { \circ } - 55 ^ { \circ } = - 25 ^ { \circ } The power factor is given by \mathrm { pf } = \cos ( heta ) = \cos \left( - 25 ^ { \circ } ight) = 0.906308 The average power is P = \frac { V _ { m } I _ { m } } { 2 } p f = 761.29854 \mathrm {~W} The reactive power is Q = \frac { V _ { m } I _ { m } } { 2 } \sin ( heta ) = - 354.99934 \mathrm { VAR } The complex power is given by \mathbf { S } = \mathrm { P } + \mathrm { jQ } = 761.29854 - \mathrm { j } 354.99934 = 840 \angle - 25 ^ { \circ } \mathrm { VA } The apparent power is given by | \mathrm { S } | = 840 \mathrm { VA } \begin{array}{l} \mathbf{Z}=\mathbf{V} / \mathbf{I}=10.5736-\mathrm{j} 4.93055 \Omega \ \mathrm{R}=10.5736 \Omega \ \mathrm{X}=-4.93055 \Omega \ \mathrm{C}=-1 /(\omega \mathrm{X})=537.98954 \mathrm{uF} \end{array}$

\begin{array}{l}\mathbf{Z}=\mathbf{V} / \mathbf{I}=10.5736-\mathrm{j} 4.93055 \Omega \\mathrm{R}=10.5736 \Omega \\mathrm{X}=-4.93055 \Omega \\mathrm{C}=-1 /(\omega \mathrm{X})=537.98954 \mathrm{uF}\end{array}

Given the Following Voltage and Current on the Load, Find

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