How is current calculated in a three-phase circuit when line voltage V_LL and power P are known (PF = 1)?

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Multiple Choice

How is current calculated in a three-phase circuit when line voltage V_LL and power P are known (PF = 1)?

In a balanced three-phase system, real power relates to line voltage, line current, and power factor by P = √3 V_LL I_L cosφ. When the power factor is 1, cosφ = 1, so the equation becomes P = √3 V_LL I_L. Solving for the current gives I_L = P / (√3 V_LL). This shows why the correct expression is the one that divides P by both the square root of 3 and the line voltage. The other forms either drop the √3 factor, invert it, or multiply by √3, which would yield incorrect current values for the same P and V_LL.

In a balanced three-phase system, real power relates to line voltage, line current, and power factor by P = √3 V_LL I_L cosφ. When the power factor is 1, cosφ = 1, so the equation becomes P = √3 V_LL I_L. Solving for the current gives I_L = P / (√3 V_LL). This shows why the correct expression is the one that divides P by both the square root of 3 and the line voltage. The other forms either drop the √3 factor, invert it, or multiply by √3, which would yield incorrect current values for the same P and V_LL.

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