Problem — Transformers with direct current

Problem

An ideal transformer has its primary connected to a $12\ \text{V}$ battery. What does a voltmeter connected to the secondary read? Discuss in five lines.

Solution

A transformer transfers voltage to the secondary only thanks to the changing magnetic flux that the primary produces in the core: the induced EMF on the secondary is $E_2=-N_2\,\dd\Phi/\dd t$, so it requires $\dd i/\dd t\neq 0$.

With a battery (direct current), at steady state the current in the primary is constant: $\dd i/\dd t=0$, the flux does not change, and the voltmeter on the secondary reads zero.

Non-zero voltages are observed only during transients: a spike on connection (the current rises quickly from $0$ to the steady-state value) and a spike on disconnection (the current drops to $0$). In both cases $\dd i/\dd t$ is large and an impulsive induced EMF appears.

$\ev{V_2=0\ \text{at steady state (DC)};\quad \text{spikes only on closing and opening}}$

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Topics: Induzione elettromagnetica Concepts: Legge di Faraday-Neumann-Lenz · Induttanza e autoinduzione