State the principle of a transformer. With a labelled diagram, explain its working, derive the ratio of voltages and currents, and list the main energy losses.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · State the principle. Mutual induction: an alternating current in the primary induces an emf in the secondary through a common core.
2 · Draw the diagram. [Laminated soft iron core; primary of Nₚ turns joined to an AC source; secondary of Nₛ turns joined to a load; flux arrows]
3 · Derive the voltage ratio. vₚ = −Nₚ dΦ/dt and vₛ = −Nₛ dΦ/dt, so vₛ/vₚ = Nₛ/Nₚ.
4 · Derive the current ratio. For an ideal transformer, iₚvₚ = iₛvₛ, so iₛ/iₚ = Nₚ/Nₛ.
5 · List the losses.
Flux leakage: wind the coils one over the other.
Copper loss: use thick wires.
Eddy currents: use a laminated core.
Hysteresis: use a low-loss soft iron core.
6 · Real life. Distribution transformers step the supply down to 220 V for homes.
7 · Close in one line. So, a transformer changes voltage and current in inverse ratio, keeping the power almost the same.
Scoring tip: Say 'ideal transformer' before writing iₚvₚ = iₛvₛ, and name the assumptions.
