Induction vs. steady sources – Does a dc source produce induced voltage? Statement: “An induced voltage is produced as a result of a dc voltage.”

Introduction / Context:
Induced voltage (emf) arises from changing magnetic flux linkage. This question draws a line between steady dc conditions and the dynamic changes required for induction, which is crucial when reasoning about transformers and inductors.

Given Data / Assumptions:

• “Induced voltage” refers to Faraday-law emf: e = − dλ/dt.
• “dc voltage” means a constant (time-invariant) source after transients have decayed.
• We consider ideal elements unless otherwise noted.

Concept / Approach:

A constant dc source produces constant currents and constant magnetic flux in steady state (ignoring saturation and temperature drift). Since dλ/dt = 0 in steady state, the induced emf is zero. Only when the current or flux changes—such as at the moment of switching on/off or during a ramp—does induction occur. Therefore, the statement as written (implying steady dc) is false.

Step-by-Step Solution:

Verification / Alternative check:

Transformers do not pass dc: a constant primary current produces no time-varying flux in steady state, so no sustained secondary emf is induced.

Why Other Options Are Wrong:

“True” is incorrect in steady state. “True only if the dc source is very large” is irrelevant—magnitude does not substitute for d/dt. “True only during switching transients” is contextually right, but the statement under test lacks that qualifier; hence the correct evaluation is False.

Common Pitfalls:

Assuming “voltage causes induction” by itself; it is the time variation of flux linkage that matters.

Final Answer:

False.