Why does a transformer only work with AC, not DC?

A conventional transformer requires changing magnetic flux. Alternating current continuously changes the magnetic field in the transformer core, so the flux linking the secondary coil changes and an emf is induced. Steady direct current eventually produces a constant magnetic field, making the rate of change of flux zero and therefore producing no sustained secondary voltage.

There is one important qualification: a transformer can respond to switched, pulsed, or otherwise varying DC. It is not the current direction alone that matters, but whether the magnetic flux changes with time. This distinction makes the explanation more accurate and helps avoid several common errors in IB Physics electromagnetism questions.

The short physics explanation

A transformer contains two coils wound around a shared magnetic core:

• The primary coil is connected to the input supply.
• The secondary coil is connected to the output circuit or load.
• The core provides a low-reluctance path that helps magnetic flux produced by the primary link the secondary.

The operating sequence is:

1. A changing input voltage produces changing magnetic flux in the core.
2. That changing flux links the secondary turns.
3. Faraday's law says that changing flux linkage induces an emf.
4. If the secondary circuit is closed, the induced emf drives a current through the load.

With an AC supply, this sequence continues throughout every cycle. With a steady DC supply, the flux changes only briefly when the supply is connected or disconnected. Once the DC conditions become steady, the flux stops changing and the secondary emf becomes zero.

Faraday's law is the central principle

The reason transformers need AC follows directly from Faraday's law of electromagnetic induction:

$$\varepsilon=-N\frac{d\Phi}{dt}$$

Here:

• $\varepsilon$ is the induced emf in volts
• $N$ is the number of turns in the coil
• $\Phi$ is the magnetic flux through one turn in webers
• $d\Phi/dt$ is the rate at which the flux changes

The negative sign represents Lenz's law. The induced emf acts in a direction that opposes the change in flux producing it. RevisionDojo's D.4.1 electromagnetic induction notes review both Faraday's law and the meaning of this negative sign.

The essential condition is therefore not simply “a magnetic field.” It is a changing magnetic flux linkage. A strong but constant magnetic field gives $d\Phi/dt=0$, so it does not produce a sustained induced emf in a stationary secondary coil.

For a coil in a uniform field, magnetic flux can be written as:

$$\Phi=BA\cos\theta$$

Flux can change if the field strength $B$, coil area $A$, or orientation $\theta$ changes. In a stationary transformer, the coil geometry does not change. The input electrical supply instead changes the field strength and direction inside the core.

Why AC produces a continuous transformer output

An alternating voltage reverses polarity periodically. In normal transformer operation, this creates magnetic flux that repeatedly increases, decreases, reverses, and increases in the opposite direction.

For a sinusoidal flux:

$$\Phi=\Phi_0\sin(\omega t)$$

Faraday's law then gives:

$$\varepsilon=-N\omega\Phi_0\cos(\omega t)$$

The induced emf is also alternating. Notice that the emf depends on the rate of change of flux, not simply its instantaneous value. When the flux is momentarily at a maximum or minimum, its rate of change is zero, so the induced emf is zero at that instant. When the flux passes through zero most rapidly, the magnitude of the induced emf is greatest.

This is a common exam distinction:

• Maximum flux does not mean maximum induced emf.
• Maximum rate of change of flux means maximum induced emf.

The RevisionDojo D.4.2 applications of electromagnetic induction notes develop the same relationship for rotating coils and other induction applications.

What happens when DC is connected to a transformer?

Suppose a battery is connected directly across the primary of a real transformer. The behaviour occurs in stages rather than all at once.

A brief output appears at switching

Immediately after the DC supply is connected, the current does not jump instantly to its final value because the primary winding has self-inductance. As the current changes, the magnetic flux changes, so a temporary emf is induced in the secondary.

Once the current and flux settle, however:

$$\frac{d\Phi}{dt}=0$$

Therefore:

$$\varepsilon_s=-N_s\frac{d\Phi}{dt}=0$$

A second transient occurs when the supply is disconnected because the magnetic field collapses. The change can be rapid, producing a large induced emf. This is why inductive circuits may require protective components to control switching voltage spikes.

Why the primary winding can overheat

Under AC operation, the changing flux induces an emf in the primary itself. By Lenz's law, this induced emf opposes the applied voltage and helps limit the current. In circuit language, the primary has substantial inductive impedance at a non-zero AC frequency.

For steady DC, the frequency is zero, so the inductive reactance is:

$$X_L=2\pi fL=0$$

After the transient, the current is limited mainly by the winding's relatively small resistance:

$$I\approx\frac{V}{R}$$

This current may be much greater than the transformer's rated current. The resulting power dissipation, $P=I^2R$, heats the winding and can damage its insulation.

A sustained DC voltage also drives the core flux in one direction. The core may enter magnetic saturation, where a further increase in magnetizing force produces relatively little additional flux. Saturation reduces the effective inductance and can allow the current to rise even more sharply. MIT OpenCourseWare describes this as a transformer volt-second limit, because the flux is related to the time integral of the applied voltage.

For safety, students should never test this by connecting a transformer directly to a battery or mains supply. Transformer circuits can produce hazardous currents and high switching voltages even when the nominal source voltage appears modest.

AC and DC compared

The phrase “transformers work with AC but not DC” is therefore useful shorthand, but the more precise statement is:

A transformer requires time-varying magnetic flux and therefore cannot transfer continuous power from a steady DC input without first converting or switching that input.

How the turns ratio follows from changing flux

In an ideal transformer, nearly the same core flux links every turn of both windings. Applying Faraday's law to each winding gives:

$$V_p=N_p\left|\frac{d\Phi}{dt}\right|$$

and

$$V_s=N_s\left|\frac{d\Phi}{dt}\right|$$

Dividing the equations produces the ideal transformer relationship:

$$\frac{V_s}{V_p}=\frac{N_s}{N_p}$$

A transformer is:

• Step-up if $N_s>N_p$, giving $V_s>V_p$

For an ideal transformer, power is conserved:

$$V_pI_p=V_sI_s$$

Consequently:

$$\frac{I_s}{I_p}=\frac{N_p}{N_s}$$

Stepping up voltage steps down current, while stepping down voltage permits a larger secondary current. Real transformers are not perfectly efficient because of winding resistance, eddy currents, magnetic hysteresis, leakage flux, and other losses.

These equations presuppose the shared, changing flux required by Faraday's law. Substituting a steady DC voltage into the turns-ratio equation and predicting a steady secondary voltage is therefore a conceptual error. The equation describes transformer action under suitable time-varying conditions, not arbitrary constant inputs.

Worked IB-style example

An ideal transformer has 600 primary turns and 150 secondary turns. A sinusoidal AC voltage of 240 V rms is applied to the primary.

The secondary voltage is:

$$V_s=V_p\frac{N_s}{N_p}$$ $$V_s=240\times\frac{150}{600}=60\text{ V rms}$$

The transformer is step-down because the secondary has fewer turns. If the same primary were connected to a 240 V DC supply, it would not provide a sustained 60 V secondary output. There could be a brief switching pulse, followed by zero secondary emf and potentially destructive primary current.

This last sentence is often the part an exam explanation needs. A correct numerical turns-ratio calculation does not replace the physical requirement for changing magnetic flux.

Why frequency matters as well as voltage

A transformer must be operated near its designed voltage and frequency. For a sinusoidal waveform, the rms emf is commonly written as:

$$E_{\text{rms}}=4.44fN\Phi_{\max}$$

Rearranging shows that, for a fixed applied voltage and number of turns:

$$\Phi_{\max}\propto\frac{V}{fN}$$

Reducing frequency while keeping voltage unchanged increases the peak core flux. If the frequency becomes too low, the core can saturate and the magnetizing current can become excessive. DC is the limiting case where $f=0$, although the sinusoidal rms equation should not simply be evaluated by inserting zero because normal sinusoidal steady-state transformer operation no longer exists.

This frequency dependence explains why a transformer rated for one AC frequency cannot automatically be operated at the same voltage on a much lower frequency. Voltage, frequency, turns, core area, and allowable flux density are connected design quantities.

Can a transformer ever be used with a DC source?

A transformer can be part of a circuit powered by DC, but the DC must first be switched so that the primary sees a changing voltage. Electronic power supplies commonly use transistors to turn DC on and off rapidly, creating pulses or an alternating waveform.

The sequence is then:

1. A DC source supplies an electronic switching circuit.
2. The switches create a time-varying primary voltage.
3. The transformer transfers energy through changing magnetic flux.
4. The secondary output may be rectified and filtered back into DC.

A square wave, pulse train, or alternating bipolar waveform can all operate a suitably designed transformer. Pure sine-wave AC is not the only possibility. The design must nevertheless prevent a net DC component from building flux in one direction and saturating the core.

This is why saying “a transformer needs changing current or changing flux” is better than saying it needs electrons to reverse direction. A pulsed unidirectional current can create changing flux, although the waveform, switching intervals, and core reset conditions must be controlled.

How to answer this in an IB Physics exam

Under the current IB Physics course, first assessed in 2025, D.4 Induction is HL-only. The official subject brief identifies D.4 within the Fields theme, while transformer questions provide a direct application of Faraday's law, flux linkage, and Lenz's law. The broader context is summarized in IB Physics Fields (HL) Explained: Exam Guide, RevisionDojo's topic-wide exam-focused guide.

For a concise “explain why” response, use a complete causal chain:

1. AC in the primary produces continuously changing magnetic flux in the core.
2. The changing flux links the secondary winding.
3. By Faraday's law, this changing flux linkage induces an emf in the secondary.
4. Steady DC produces constant flux after the switching transient, so $d\Phi/dt=0$ and no sustained secondary emf is induced.
5. DC may also cause excessive primary current, core saturation, and heating because the winding has no steady-state inductive reactance.

A four-mark question may reward these as separate marking points. Do not stop at “AC changes direction,” because that does not explicitly connect the input to magnetic flux and induced emf.

For further preparation, use the D.4 Induction lessons to review the theory, then attempt the D.4 Induction Questionbank. The electromagnetic induction flashcards are useful for recalling definitions, while Jojo AI can help identify missing links in written explanations.

Common mistakes to avoid

Saying that DC creates no magnetic field

DC does create a magnetic field. The problem is that, after the transient, the field is constant and therefore does not induce a sustained secondary emf.

Saying that only a changing magnetic field matters

The more precise quantity is magnetic flux linkage. Flux depends on field strength, area, orientation, and the number of turns linked by the field.

Ignoring the switching transient

Connecting or disconnecting DC changes the flux, so a brief secondary emf can appear. It is sustained DC operation that fails to produce continuous transformer action.

Applying the turns ratio to steady DC

The ideal turns-ratio equation is derived from Faraday's law under shared changing flux. It cannot be used to predict a continuous secondary voltage from a constant primary voltage.

Claiming that the core creates energy

The core guides and strengthens magnetic coupling, but it is not an energy source. Energy delivered to the secondary ultimately comes from the primary supply, consistent with Lenz's law and conservation of energy.

Conclusion

A transformer needs AC because transformer action depends on changing magnetic flux, not merely the presence of current or a magnetic field. AC maintains changing flux and therefore a continuous induced emf in the secondary, while steady DC produces only brief switching transients before the secondary emf falls to zero.

Applying DC directly can also saturate the core, produce excessive primary current, and overheat the winding. For exam preparation, practise expressing the full chain from alternating input to changing flux to induced emf. RevisionDojo's D.4 notes, Questionbank, Flashcards, and Jojo AI are useful for checking both the equations and the precision of your written explanations.

Sources and referenced URLs

• IB Diploma Programme Physics subject brief, first assessment 2025
• OpenStax University Physics: Faraday's law
• OpenStax University Physics: Transformers
• MIT OpenCourseWare: Magnetics and transformer volt-second limits
• RevisionDojo: IB Physics Fields (HL) Explained
• RevisionDojo: D.4.1 Principles of electromagnetic induction notes
• RevisionDojo: D.4.2 Applications of electromagnetic induction notes
• RevisionDojo: D.4 Induction lessons
• RevisionDojo: D.4 Induction Questionbank
• RevisionDojo: Electromagnetic induction flashcards