Turns ratio needed to step 120 V AC up to 900 V AC using an ideal transformer.

Introduction / Context:
Determining the turns ratio from desired input and output voltages is a routine transformer design task. The ideal transformer voltage ratio equals the turns ratio Ns/Np.

Given Data / Assumptions:

• Input (primary) voltage Vp = 120 V AC.
• Desired output (secondary) voltage Vs = 900 V AC.
• Ideal transformer; Vs/Vp = Ns/Np.

Concept / Approach:
For ideal transformers: turns ratio r = Ns/Np = Vs/Vp. Compute the numeric ratio and choose the closest exact option.

Step-by-Step Solution:
r = Vs/Vp = 900 / 120r = 7.5

Verification / Alternative check:
Check proportionality: 120 V × 7.5 = 900 V, confirming that a 7.5:1 step-up is required.

Why Other Options Are Wrong:

• 75 or 750: Excessive step-up, yielding tens of kilovolts.
• 0.13: This would step down, not up.

Common Pitfalls:
Inverting the ratio or mixing up primary and secondary, which would give 0.133 instead of 7.5. Always compute Vs/Vp for Ns/Np when stepping up the voltage.

Final Answer:
7.5