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Difficulty: MediumFundamentals of Electromagnetism and Induction

A transformer is constructed with 500 turns on its primary coil and 100 turns on its secondary coil. If a technician connects a steady 12 V direct current (DC) source across the primary coil, what continuous voltage is measured across the open secondary terminals?

  1. A
    2.4 V
  2. 0 VAnswer
  3. C
    12 V
  4. D
    60 V

Answer

0 V
A continuous voltage of 0 V is measured because electromagnetic induction requires a changing magnetic flux (dΦdt\frac{d\Phi}{dt}) to induce an electromotive force in a secondary conductor. Because a steady direct current creates a stationary, unchanging magnetic field, mutual induction cannot occur continuously.

Step-by-Step Solution

1
Analyze the type of electrical source applied to the primary coil
The input source provides a steady direct current (DC) of 12 V.
Electromagnetic induction depends fundamentally on whether the source produces a changing or constant current.
2
Evaluate the magnetic field produced by the steady DC input
The steady current creates a static, unchanging magnetic field within the transformer core.
According to Ampere's law, a constant current generates a constant magnetic flux (dΦdt=0\frac{d\Phi}{dt} = 0).
3
Apply Faraday's Law of Electromagnetic Induction to determine the secondary voltage
The induced voltage across the secondary coil is Vs=−NsdΦdt=0 VV_s = -N_s \frac{d\Phi}{dt} = 0\text{ V}.
Faraday's law states that an induced electromotive force requires a changing magnetic flux through the coil.

Key Concept

Faraday's Law of Induction and Transformer Operation on DC vs. AC
Estimated Time:45s
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Topics

Fundamentals of Electromagnetism and Induction

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