Transformer design: If 120 V (RMS) is applied to a 2400-turn primary, how many turns are required on the secondary to obtain 7.5 V (RMS) at the secondary?

Introduction / Context:
The transformer turns ratio directly sets the voltage ratio between windings in the ideal case. Designing low-voltage secondaries (for logic supplies, heaters, or instrumentation) requires correctly scaling turns from a known primary.

Given Data / Assumptions:

• Primary voltage Vp = 120 V RMS.
• Primary turns Np = 2400 turns.
• Desired secondary voltage Vs = 7.5 V RMS.
• Ideal transformer approximation (no regulation drop).

Concept / Approach:
In an ideal transformer, Vs/Vp = Ns/Np. Therefore, Ns = Np * (Vs/Vp). This linear proportionality allows immediate calculation of required secondary turns for a target voltage.

Step-by-Step Solution:
Compute ratio: Vs/Vp = 7.5 / 120 = 0.0625.Apply to turns: Ns = 2400 * 0.0625 = 150 turns.Thus, 150 turns on the secondary will yield approximately 7.5 V RMS.

Verification / Alternative check:
Reverse-check: Ns/Np = 150/2400 = 1/16; applying to voltage gives Vp/16 = 120/16 = 7.5 V. Agreement confirms the result.

Why Other Options Are Wrong:
75 turns would produce 3.75 V; 900 turns would produce 45 V; 1920 turns would give 96 V; 15 turns would give 0.75 V. None match the target 7.5 V.

Common Pitfalls:
Confusing turns ratio with impedance ratio. Voltages scale linearly with turns; impedances scale with the square of the turns ratio.

Final Answer:
150 turns