Transformer design goal: What primary voltage is required if a transformer with turns ratio Np/Ns = 0.1 must produce a 9 V secondary output?

Introduction / Context:
This question tests your ability to manipulate the transformer voltage–turns relation when the turns ratio is given as a single number Np/Ns, not as a colon pair. It is common in datasheets and calculations to express the ratio this way.

Given Data / Assumptions:

• Turns ratio r = Np/Ns = 0.1.
• Desired secondary voltage Vs = 9 V (RMS).
• Ideal transformer; ignore losses and regulation.

Concept / Approach:
Voltage ratio equals turns ratio: Vp / Vs = Np / Ns. Rearranging gives Vp = Vs * (Np/Ns). When the turns ratio is less than 1, the transformer is step-up (secondary has more turns than primary), so the required primary voltage is lower than the secondary voltage.

Step-by-Step Solution:

Verification / Alternative check:
If Vp = 0.9 V and Np/Ns = 0.1, then Vs = Vp / (Np/Ns) = 0.9 / 0.1 = 9 V, confirming consistency.

Why Other Options Are Wrong:

• 90 V and 900 V: These imply step-down assumptions; they invert the ratio.
• 9 V: Would only be correct if Np = Ns (ratio 1).
• 18 V: Unrelated to the required 9 V with the given ratio.

Common Pitfalls:

• Confusing Np/Ns with Ns/Np; always match Vp/Vs = Np/Ns.
• Forgetting the problem states Np/Ns = 0.1, not Ns/Np.

Final Answer:
0.9 V