Why a Transformer Does Nothing on DC

A transformer has no moving parts and no electrical connection between its two coils — power gets from the primary to the secondary without a single electron crossing over. That alone should raise the question of what exactly is doing the work. The answer is the magnetic flux threading through both coils, and that answer immediately tells you why DC fails: the mechanism doesn’t run on flux existing, it runs on flux changing.

Mutual induction needs a changing flux, not just a flux

Current in the primary coil sets up a magnetic field, and the iron core common to both coils channels that field so that nearly all of it also passes through the secondary coil as flux, Φ. Faraday’s law of electromagnetic induction says the EMF induced in the secondary is

ε = −N (dΦ/dt)

Read this literally: the induced EMF depends on the rate of change of flux, not on the flux itself. A secondary coil sitting in a large, perfectly constant flux has dΦ/dt = 0 and therefore zero induced EMF, no matter how strong that flux is. This isn’t a limitation of real transformers — it’s the content of the law. Mutual induction is fundamentally a response to change, the same way a capacitor’s current is a response to changing voltage rather than to voltage itself.

AC keeps the flux changing; steady DC lets it settle

Feed the primary an alternating current and the current itself is continuously rising, falling, and reversing direction, so the flux it produces does exactly the same — it’s never constant, which means dΦ/dt never settles to zero, which means the secondary has a continuously induced EMF, oscillating at the same frequency as the primary current. That alternating EMF is the entire output of the device.

Feed the primary a steady DC voltage instead, and immediately after switch-on there genuinely is a changing flux — the current is ramping up from zero toward its steady value, so the secondary does show a brief induced pulse at that instant, which is itself proof the law is behaving exactly as expected. But once the primary current reaches its steady DC value and stays there, the flux it produces is constant too. With dΦ/dt = 0 from that point on, the induced EMF in the secondary drops to exactly zero and stays there for as long as the DC remains steady. The transformer hasn’t failed or switched off some special DC-blocking mechanism; Faraday’s law has simply returned the only answer it can return once nothing is changing.

This is also why real transformers are rated by frequency and why a transformer designed for mains AC would, if fed DC for any length of time, mainly just overheat the primary winding from the resulting large steady current — with none of the induction effect to show for it, since the induction was never about the current’s size in the first place, only about how fast it was changing.

It’s worth being precise about what “DC” means in this argument, because the common follow-up question — “but current was flowing, wasn’t it?” — conflates two different things. Current flowing is not the same as current changing. A transformer’s secondary responds only to the second one. You could run an enormous, perfectly steady DC current through the primary, building a correspondingly enormous and perfectly steady flux, and the secondary would still read zero, because dΦ/dt only measures how fast that flux is changing, never how large it is. This is also why switching a DC supply on and off repeatedly — effectively chopping it into a crude square wave — does induce a secondary EMF: you’ve reintroduced the one ingredient that matters, a flux that changes with time, even though the source itself never stopped being “DC” in the sense of never reversing polarity.

The complete treatment of transformers — turns ratio, step-up versus step-down operation, and the efficiency losses real devices have to account for — is in the Alternating Current notes.