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The per-unit impedance of an alternator corresponding to base values 13.2 kV and 30MVA is 0.2 p.u. The p.u. value of the impedance for base values 13.8 kV and 50 MVA in p.u.will be
  • a)
    0.131
  • b)
    0.226
  • c)
    0.305
  • d)
    0.364
Correct answer is option 'C'. Can you explain this answer?
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The per-unit impedance of an alternator corresponding to base values 1...
Given data:
- Per-unit impedance of the alternator for base values 13.2 kV and 30 MVA = 0.2 p.u.
- New base values: 13.8 kV and 50 MVA

To find: Per-unit impedance for new base values

Solution:

Step 1: Calculate the per-unit impedance for the given base values using the formula:

Z_base = V_base^2 / S_base

where,
Z_base = per-unit impedance at base values
V_base = base voltage in kV
S_base = base apparent power in MVA

For the given base values of 13.2 kV and 30 MVA,

Z_base = (13.2 kV)^2 / 30 MVA
= 5.76 Ω

Per-unit impedance at base values = Z_base / Z_base
= 5.76 Ω / 5.76 Ω
= 1 p.u.

Step 2: Calculate the per-unit impedance for new base values using the formula:

Z_new = Z_base * (V_new / V_base)^2 / (S_new / S_base)

where,
Z_new = per-unit impedance for new base values
V_new = new base voltage in kV
S_new = new base apparent power in MVA

Substituting the given values,

Z_new = 1 * (13.8 kV / 13.2 kV)^2 / (50 MVA / 30 MVA)
= 0.305 p.u.

Therefore, the per-unit impedance for new base values of 13.8 kV and 50 MVA is 0.305 p.u., which is option (c).
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The per-unit impedance of an alternator corresponding to base values 13.2 kV and 30MVA is 0.2 p.u. The p.u. value of the impedance for base values 13.8 kV and 50 MVA in p.u.will bea)0.131b)0.226c)0.305d)0.364Correct answer is option 'C'. Can you explain this answer?
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