Question

(i) Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three causes for energy losses in a real transformer.
(ii) A step-up transformer converts a low voltage into high voltage. Does it violate the principle of conservation of energy? Explain.
(iii) A step-up transformer has 200 and 3000 turns in its primary and secondary coils respectively. The input voltage given to the primary coil is 90V. Calculate:
1. The output voltage across the secondary coil.
2. The current in the primary coil if the current in the secondary coil is 2.0A.

Hint:

- A step-up transformer% increases voltage by having more turns in the secondary coil than the primary coil.
- It operates on Faraday’s Law of Electromagnetic Induction, where a varying magnetic flux induces an EMF in the secondary coil: \[ \mathcal{E} = - \frac{d\Phi_B}{dt} \] - The voltage ratio follows the turns ratio formula: \[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \] - Energy Losses in Transformers: - Eddy Current Losses: Minimized using laminated cores. - Hysteresis Losses: Reduced using soft magnetic materials. - Copper Losses: Reduced by using low-resistance wire.

Answer 1

Step-Up Transformer
A step-up transformer increases the voltage by having more turns in the secondary coil compared to the primary coil.
Working Principle:
A step-up transformer works on the principle of electromagnetic induction. When an alternating current flows through the primary coil, it generates a varying magnetic flux in the core. This varying flux induces an electromotive force (EMF) in the secondary coil according to Faraday's Law: \[ \mathcal{E} = -\frac{d\Phi_B}{dt}. \] The voltage ratio between the primary and secondary coils is given by the turns ratio: \[ \frac{V_s}{V_p} = \frac{N_s}{N_p}. \] Energy Losses in Transformers: % Option (A) Eddy Current Losses: Circulating currents in the core produce heat, reducing efficiency. These are minimized by using laminated cores. % Option (B) Hysteresis Losses: Energy is lost during repeated magnetization and demagnetization of the core. Soft magnetic materials help reduce this loss. % Option (C) Copper Losses: Heat is generated due to the resistance of the windings. This can be reduced by using low-resistance materials for the coils.