DC on transformers again: A 6 V battery is connected across the primary of a transformer with turns ratio 8 (Np/Ns or 8:1). What steady-state secondary voltage results?

Introduction / Context:
Transformers need time-varying magnetic fields to induce a secondary voltage. A DC battery, after a brief switching transient, produces no sustained change in flux, so no sustained induced secondary voltage appears. This question reinforces that concept.

Given Data / Assumptions:

• Primary excitation is DC: 6 V battery.
• Turns ratio magnitude 8 (step-down or step-up irrelevant for DC steady state).
• Steady-state condition after initial connection transient.

Concept / Approach:
Induced EMF magnitude is proportional to dΦ/dt. With DC, dΦ/dt → 0 as current stabilizes; therefore, Vs → 0 V in steady state. (Practical note: continuous DC can overheat the primary and saturate the core; this is outside the scope of the numeric answer.)

Step-by-Step Solution:

Verification / Alternative check:
An oscilloscope would show a spike at connection then decay to zero volts on the secondary, confirming the reasoning.

Why Other Options Are Wrong:

• 6 V, 48 V, 0.75 V: These apply AC ratio logic to DC, which is invalid at steady state.
• 24 V: Also misapplies the turns relation to DC.

Common Pitfalls:

• Using the turns ratio directly on DC values.
• Ignoring transient versus steady-state distinction.

Final Answer:
0 V