Examkin

Question

Difficulty: MediumInductors and Transformers

A step-down transformer has a 10:110:1 turns ratio between its primary and secondary windings. If the primary winding is connected across a steady 12 V12\text{ V} direct current (DC) power supply, what voltage is measured across the secondary winding under steady-state conditions?

  1. A
    1.2 V1.2\text{ V}
  2. B
    12 V12\text{ V}
  3. 0 V0\text{ V}Answer
  4. D
    120 V120\text{ V}

Answer

0 V0\text{ V}
Transformers operate through mutual electromagnetic induction, requiring an alternating current (AC) to generate an expanding and collapsing magnetic field. A steady direct current (DC) produces a static, unvarying magnetic field once the circuit reaches steady state. Because Faraday's Law requires a changing magnetic field (ΔΦΔt≠0\frac{\Delta\Phi}{\Delta t} \neq 0) to induce an electromotive force, the secondary winding produces exactly 0 V0\text{ V}.

Step-by-Step Solution

1
Identify the type of input voltage applied to the transformer primary winding.
The input source is a steady 12 V12\text{ V} direct current (DC) supply.
Transformers rely on mutual electromagnetic induction, which fundamentally requires a time-varying magnetic field.
2
Analyze the magnetic flux created in the core during steady-state DC operation.
A steady DC current produces a stationary, unchanging magnetic flux (ΔΦΔt=0\frac{\Delta\Phi}{\Delta t} = 0).
According to Faraday's Law of Induction, voltage is only induced in a conductor when magnetic flux lines expand or collapse across the winding turns.
3
Determine the resulting secondary output voltage.
The induced secondary voltage is 0 V0\text{ V}.
With zero rate of change of magnetic flux in steady state, no electromotive force (EMF) is induced in the secondary winding.

Key Concept

Transformers require alternating current (AC) to induce a secondary voltage via changing magnetic flux; steady direct current (DC) produces no secondary voltage.
Estimated Time:1m 0s
Rate this question

Topics

Inductors and Transformers

More questions from this topic