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A balanced, three phase, {VLINE} V system is supplying a load connected in {type}.

{image('resources/question-resources/'+Circuit)}

The loads are:

$Z_1 = \\var{R1}+i\\ \\var{X1}\\ \\Omega $

$Z_2 = \\var{R2}+i\\ \\var{X2}\\ \\Omega $

$Z_3 = \\var{R3}+i\\ \\var{X3}\\ \\Omega $

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Rated Voltage

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Phase Voltage

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index for the connection type:

0 = star with a neutral

1 = delta

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Line Current

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Line Current

", "templateType": "anything"}, "IC": {"name": "IC", "group": "Currents", "definition": "(1-StarorDelta)*I3 + StarorDelta*(I2-I1)", "description": "

Line Current

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Load Current

", "templateType": "anything"}, "I2": {"name": "I2", "group": "Currents", "definition": "V2/(R2+X2*i)", "description": "

Load Current

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Load Current

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What is the load voltage? [[0]] V

Using $V_A$ as the reference voltage, calculate the currents in each load:

$I_1 = $[[1]]$\\angle$ [[2]]$^o$ A

$I_2 = $[[3]]$\\angle$ [[4]]$^o$ A

$I_3 = $[[5]]$\\angle$ [[6]]$^o$ A

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Use Complex Numbers throughout.
Use Ohm's Law.

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Determine the currents in each line:

$I_A = $[[0]]$\\angle$ [[1]]$^o$ A

$I_B = $[[2]]$\\angle$ [[3]]$^o$ A

$I_C = $[[4]]$\\angle$ [[5]]$^o$ A

Use Complex Numbers throughout.
Use Kirchhoff's Current Law.

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Determine the real power flowing in each line:

$P_A = $[[0]]W

$P_B = $[[1]]W

$P_C = $[[2]]W

Use Complex Numbers throughout (but the final answer is real).
Real power is the real part of the voltage times the current.

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Determine the real power flowing in each load:

$P_1 = $[[0]]W

$P_2 = $[[1]]W

$P_3 = $[[2]]W

Use Complex Numbers throughout (but the final answer is real).
Real load power is used only in resistances.

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