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Three-Phase Motor Current from Output Power and Efficiency

A 50 kW, 400 V, 3 phase synchronous motor is operating at full load with an efficiency of 90%. If the field current is adjusted to make its power factor 0.8 leading, estimate the armature current.

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Answer & Explanation

Correct AnswerC. 100 A

Quick Explanation

C — 100 A approximately. Electrical input is 50/0.90 = 55.56 kW, giving line current 55,555.56/(√3 × 400 × 0.8) = 100.23 A.

Formula / Key Relation

I_L = P_out/(η√3 V_Lcos φ)

I_L = 50,000/(0.90 × √3 × 400 × 0.8) = 100.23 A

Detailed Explanation

Correct answer: C — 100 A

Given data and required current

The motor delivers 50 kW shaft output at full load. Its efficiency is 0.90, line voltage is 400 V, and power factor is 0.8 leading. The three-phase power equation uses electrical input power, so the shaft output must first be converted to input.

Step 1: Calculate electrical input power. Efficiency is output power divided by input power:

η = P_out/P_in

P_in = 50,000/0.90 = 55,555.56 W

Step 2: Write the balanced three-phase power equation. Using line voltage and line current:

P_in = √3 V_LI_Lcos φ

I_L = P_in/(√3 V_Lcos φ)

Step 3: Substitute the values. Keep power in watts and voltage in volts to obtain amperes:

I_L = 55,555.56/(√3 × 400 × 0.8)

I_L = 100.23 A ≈ 100 A

Therefore, the matching answer is C — 100 A. A leading power factor means the current leads the voltage; it does not change the magnitude calculation because cos φ = 0.8.

The result is the line current, conventionally intended here by armature current. Winding phase current equals line current for star connection and line current divided by √3 for delta connection. The question gives no winding connection, so a separate phase-current value cannot be determined.

Quick Trick

50/0.9≈55.6 kW; then divide by 1.732×400×0.8≈554 → about 100 A.

Why Other Options Are Wrong

138 A and 80 A do not satisfy the combined efficiency and three-phase power relation. 58 A is too low for 55.56 kW input at 400 V and 0.8 pf. C reproduces the rated output on back-substitution.

Common Mistake

Using 50 kW directly as electrical input and ignoring 90% efficiency; that would under-estimate the current.

Exam Tip

Motor: P_in=P_out/η. Generator: P_out=ηP_in. Get this direction right before calculating current.

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