Question

A transformer is designed to convert an AC voltage of 220 V to an AC voltage of 12 V. If the input terminals are connected to a DC voltage of 220 V, the transformer usually burns. Explain.

Answer 1

A transformer is ideally an inductive coil. For an inductor connected across a DC voltage,

$$\begin{gathered} V-L\frac{di}{dt}=0 \\ \Rightarrow V=L\frac{di}{dt} \\ \Rightarrow \int di=\frac{V}{L}\int dt \\ \Rightarrow i=\frac{Vt}{L} \end{gathered}$$

For a DC source, the current across the inductor will increase with time and can reach a very large value, which can burn the transformer.