Q.9 Explain the working of a transformer with a neat, labelled diagram.
Best answer
Answer:
[Figure: a laminated soft-iron core (closed rectangular frame). The primary coil P with \(N_P\) turns is wound on one limb and connected to the a.c. input \(e_P\); the secondary coil S with \(N_S\) turns is wound on the other limb and gives the a.c. output \(e_S\) across a load.]
Principle: mutual induction.
Working: An alternating voltage applied to the primary sends an alternating current through it, which produces an alternating magnetic flux in the core. The laminated core links this flux almost completely with the secondary. The changing flux induces an emf in each turn of both coils. If \(\phi\) is the flux through each turn,
\[e_P = -N_P\frac{d\phi}{dt},\qquad e_S = -N_S\frac{d\phi}{dt}\ \Rightarrow\ \frac{e_S}{e_P} = \frac{N_S}{N_P}\]If \(N_S \gt N_P\) the voltage is increased (step-up transformer); if \(N_S \lt N_P\) it is decreased (step-down transformer). For an ideal transformer the input and output powers are equal, \(e_P I_P = e_S I_S\), so \(\dfrac{I_S}{I_P} = \dfrac{N_P}{N_S}\).
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