MP Board · Class 12 · Physics · Alternating CurrentWhat is a transformer? Explain its principle, construction, and working mechanism. Describe the main types of energy losses in a real transformer and explain how each loss can be minimized.

Transformer: Definition and Principle

Definition: A transformer is a static electrical device used to convert alternating current at low voltage into high voltage (Step-up transformer) or high voltage into low voltage (Step-down transformer) without changing the frequency of the alternating source.

Principle: It works on the principle of Mutual Induction. When an alternating current flows through a primary coil, it creates a continuously changing magnetic flux in the core. This changing magnetic flux links with the secondary coil and induces an alternating electromotive force (emf) in it.

Construction and Working

• Construction:

  • Laminated Core: Made of thin rectangular or E-I shaped sheets of soft iron, insulated from each other with varnish to reduce eddy currents.
  • Primary Coil ($N_p$ turns): Connected to the input alternating voltage supply.
  • Secondary Coil ($N_s$ turns): Connected to the output load circuit.

• Working & Formula: Let $\phi$ be the magnetic flux linked with each turn at any instant. According to Faraday's Law of Electromagnetic Induction:

  • Induced emf in Primary coil: $e_p = -N_p \frac{d\phi}{dt}$
  • Induced emf in Secondary coil: $e_s = -N_s \frac{d\phi}{dt}$

  Dividing the equations: $$\frac{e_s}{e_p} = \frac{N_s}{N_p} = K$$ (where $K$ is the transformation ratio)

  • For an ideal transformer (Power Input = Power Output): $$V_p I_p = V_s I_s \implies \frac{V_s}{V_p} = \frac{I_p}{I_s} = \frac{N_s}{N_p}$$
  • Step-up Transformer: $N_s > N_p \implies V_s > V_p$ and $I_s < I_p$
  • Step-down Transformer: $N_s < N_p \implies V_s < V_p$ and $I_s > I_p$

Energy Losses in a Transformer & Remedies

1. Copper Loss (Joule Heating):

   • Cause: Heat generated ($I^2 R$) due to the resistance of copper wire windings.
   • Minimization: Use thick copper wires with low resistance for high-current windings.

2. Iron Loss / Eddy Current Loss:

   • Cause: Changing magnetic flux induces eddy currents in the iron core, causing heating.
   • Minimization: Use a laminated soft iron core coated with insulating varnish.

3. Hysteresis Loss:

   • Cause: Repeated magnetization and demagnetization of the core material during each AC cycle causes energy dissipation as heat.
   • Minimization: Use core materials with a thin hysteresis loop, such as soft iron or silicon steel.

4. Flux Leakage Loss:

   • Cause: Not all magnetic flux generated by the primary coil links with the secondary coil.
   • Minimization: Wind primary and secondary coils over each other on the same core arm.