Math Problem Statement

A single-phase transformer has 500 primary turns and 1200 secondary turns, with a primary voltage of 500 V. If the flux density is 1.5 Wb/m² and the core area is 50 cm², calculate the secondary voltage.

Solution

I see you've uploaded an image of an exam paper from Yaba College of Technology's School of Engineering, focusing on Electrical Machines II. Here’s a quick breakdown of the questions as listed in your image:

  1. Question 1:

    • (a) Discuss the principle of operation of transformers.
    • (b) Given the equation Es=4.44NsΦfE_s = 4.44N_s\Phi f, show that Es/Ep=Ns/NpE_s/E_p = N_s/N_p (related to transformer universal equation).
    • (c) A single-phase transformer has 500 primary turns and 1200 secondary turns, with a primary voltage of 500 V. If the flux density is 1.5 Wb/m² and the core area is 50 cm²:
      1. Calculate the value of flux density in the core.
      2. Calculate the secondary voltage.
  2. Question 2:

    • (a) Define terms related to electromagnetic induction: magnetic flux, flux linkage, etc.
    • (b) In a laboratory experiment to verify Faraday’s law, a coil is rotated, and the induced e.m.f. over an interval is recorded. Calculate:
      1. Magnetic flux.
      2. Average current.
  3. Question 3:

    • (a) Define self-inductance and explain mutual inductance.
    • (b) Given a transformer and several impedances, calculate:
      1. Equivalent resistance as referred to primary.
      2. Equivalent resistance as referred to secondary.
      3. Equivalent reactance as referred to both primary and secondary.
  4. Question 4:

    • (a) Draw a well-labeled electrical machine classification chart.
    • (b) Prove the energy stored in the magnetic field of a coil using the given relationship.
    • (c) State three advantages of 3-phase transformers over single-phase transformers.

Would you like a detailed explanation or step-by-step solution for any of these specific questions? Let me know if you need assistance with calculations or theory!


Here are five related questions for deeper understanding:

  1. What are the main losses in a transformer and how can they be minimized?
  2. How does the core material affect transformer efficiency?
  3. How does mutual inductance differ from self-inductance in transformers?
  4. Can you explain the relationship between voltage, current, and flux in an ideal transformer?
  5. What is the significance of phase grouping in three-phase transformers?

Tip: When calculating transformer efficiency, always account for copper and iron losses to get an accurate result.

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Math Problem Analysis

Mathematical Concepts

Transformer equations
Electromagnetic induction

Formulas

E_s = 4.44 N_s Φ f
E_s / E_p = N_s / N_p

Theorems

Faraday’s Law of Electromagnetic Induction
Transformer Ratio Theorem

Suitable Grade Level

College level - Electrical Engineering