Transformer DC

To answer this problem, we must first understand how a transformer works. A transformer is made of two coils: a primary coil and a secondary coil, wrapped around a common iron core as shown in the figure below:

As current $I_{P}$ flows through the primary coil, it generates magnetic flux $\Phi$ that is proportional to the number of turns $N_{P}$ , the current $I_{P}$ and the radius of the coil $R_{P}$ . The transformer core prevents the flux from leaking, so most of the magnetic flux of the primary coil reaches the secondary coil. By Faraday's law of Electromagnetic Induction , EMF $\mathcal{E} = V_{S} = -\frac{d\Phi}{dt}$ is generated in the secondary coil.

In order to generate a non-zero voltage in the secondary coil, $\frac{d\Phi}{dt}$ must not be zero, which implies that $\Phi$ must not be constant. In other words, $\Phi$ must vary with time. The value of $\Phi$ can be changed by changing the current in the coil. If the magnitude of current in the primary coil $I_{P}$ changes with time, then $\Phi$ also changes with time and we get useful voltage in the secondary coil. It is possible to have time-varying direct current in the primary coil, therefore a transformer can work with direct current. $_\square$

Image Credit: Wikimedia Commons BillC