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Half-wave controlled rectifier feeding a resistive load: given Vdc = 127 V at firing angle α = 0°, estimate the average output voltage when α = 30°.

Difficulty: Medium

Correct Answer: 120 V

Explanation:


Introduction / Context:
This computation applies the average voltage formula for a single-phase half-wave controlled rectifier with a resistive load. It illustrates how firing angle reduces the DC component of the output.


Given Data / Assumptions:

  • At α = 0°, Vdc0 = 127 V.
  • Load is purely resistive (no freewheeling).
  • Supply is sinusoidal with peak Vm (unknown explicitly).


Concept / Approach:
For a half-wave controlled rectifier, average output voltage is Vdc(α) = (Vm / (2π)) * (1 + cos α). When α = 0°, Vdc0 = Vm / π → Vm = π * Vdc0. We can reuse Vm to compute Vdc at α = 30° without knowing the actual mains value.


Step-by-Step Solution:

From α = 0°: Vm = π * 127.At α = 30°: Vdc(30°) = (Vm / (2π)) * (1 + cos 30°).Compute factor: (1 + cos 30°) = 1 + 0.866 ≈ 1.866.Thus Vdc(30°) = (π * 127 / (2π)) * 1.866 = 127 * 0.933 ≈ 118.5 V ≈ 120 V.


Verification / Alternative check:

A quick ratio check: Vdc(α) / Vdc0 = (1 + cos α) / 2 = (1 + 0.866) / 2 = 0.933 → 127 * 0.933 ≈ 118.5 V.


Why Other Options Are Wrong:

127 V ignores the firing delay; 110 V and 100 V correspond to larger α; 135 V exceeds the α = 0° reference and is impossible.


Common Pitfalls:

Using the full-wave formula Vdc = (Vm/π) * cos α by mistake; misapplying degrees vs radians in cosine.


Final Answer:

120 V
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