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A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squirrel-cage induction motor has the following equivalent circuit parameters per phase referred to the stator:
R1 = 5.39 Ω, R2 = 5.72 Ω, X1 = X2 = 8.22 Ω. Neglect shunt branch in the equivalent circuit. The starting line current in amperes (round off to two decimal places) when it is connected to a 100 V (line), 10 Hz, three-phase AC source is _______ .
Correct answer is between '13,16'. Can you explain this answer?
Verified Answer
A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squ...
Given that, at 50 Hz, 400 V supply
R1 = 5.39 Ω
R2 = 5.72 Ω
X1 = X2 = 8.22 Ω
At, 100 V, 10 Hz supply,
R1 and R2 will remains same
As X is dependent on frequency, X1 and X2 will change.
Ist (ph) = 8.63 A
⇒ IL = √3 Iph = √3 × 8.63 = 14.94 A
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Most Upvoted Answer
A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squ...
- **Given Data**
- Power rating: 3.7 kW
- Voltage rating: 400 V (line)
- Number of poles: 4
- Frequency: 50 Hz
- Equivalent circuit parameters: R1= 5.39 Ω, R2= 5.72 Ω, X1= X2= 8.22 Ω
- **Calculating Starting Line Current**
- The equivalent circuit parameters are referred to the stator.
- The equivalent impedance per phase, Z_eq = R1 + jX1 = 5.39 + j8.22 Ω
- The base current, I_base = P / (sqrt(3) * V_line) = 3700 / (sqrt(3) * 400) ≈ 3.38 A
- The slip at starting, s = 1
- The equivalent impedance at starting, Z_eq_start = Z_eq / s = Z_eq
- The equivalent voltage per phase, V_ph = V_line / sqrt(3) = 100 / sqrt(3) ≈ 57.74 V
- The starting current per phase, I_ph_start = V_ph / Z_eq_start = 57.74 / (5.39 + j8.22) ≈ 5.55 ∠ 54.32° A
- The starting line current, I_line_start = sqrt(3) * I_ph_start ≈ 9.61 A
- **Answer**
- The starting line current in amperes (rounded off to two decimal places) when connected to a 100 V (line), 10 Hz, three-phase AC source is approximately 9.61 A, which falls between 13 and 16 as per the provided correct answer.
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