Transformers and DC excitation: The primary of a transformer is connected to a 6 V battery (DC). Turns ratio is 1:3 and the secondary load RL = 100 Ω. What steady-state voltage is across the load?

Introduction / Context:Transformers require changing magnetic flux to induce secondary voltage. A pure DC source does not sustain changing flux after the initial transient, so understanding steady-state behavior prevents design errors and overheating scenarios.

Given Data / Assumptions:

• DC source: 6 V battery on the primary.
• Turns ratio 1:3 (primary:secondary).
• Secondary load RL = 100 Ω.
• Steady-state condition after any switching transient; idealized core behavior for concept.

Concept / Approach:Induced voltage is proportional to time rate of change of flux (Faraday’s law). With DC, after the initial connection transient, dΦ/dt → 0, so the induced secondary voltage tends to 0 V. The transformer core may saturate if DC persists, but the key answer is the steady-state secondary voltage.

Step-by-Step Solution:

Verification / Alternative check:Using the transformer equation V = N * dΦ/dt qualitatively: with constant current and constant flux (ignoring saturation), the time derivative is zero, hence no induced EMF.

Why Other Options Are Wrong:

• 6 V or 18 V or 2 V: These presume AC action or a lasting voltage ratio; not applicable with DC at steady state.
• 0.6 V: No mechanism produces this steady value without time-varying flux.

Common Pitfalls:

• Assuming the turns ratio applies to DC the same way as AC.
• Ignoring that transformers are inductive devices needing changing current.

Final Answer:0 V