Ideal transformer voltage step-up: With a turns ratio of 20 (secondary-to-primary) and a primary AC voltage of 12 V, what is the secondary voltage produced?

Introduction / Context:
This question tests the fundamental transformer relationship between turns ratio and voltage ratio in an ideal transformer. Understanding this relationship is essential for sizing transformers and predicting output voltages in power and electronics applications.

Given Data / Assumptions:

• Primary (input) voltage, Vp = 12 V AC.
• Turns ratio r = Ns/Np = 20 (secondary turns to primary turns).
• Ideal transformer (no losses), so voltage scales directly with turns.

Concept / Approach:
For an ideal transformer, the voltage ratio equals the turns ratio. Hence Vs/Vp = Ns/Np. If Ns/Np > 1, the transformer steps the voltage up. If Ns/Np < 1, it steps the voltage down.

Step-by-Step Solution:
Vs/Vp = Ns/NpVs = Vp * (Ns/Np)Vs = 12 * 20Vs = 240 V

Verification / Alternative check:
Because the secondary has twenty times as many turns as the primary, the secondary voltage must be twenty times the primary voltage. 12 V * 20 = 240 V confirms the result.

Why Other Options Are Wrong:

• 12 V: No step-up; contradicts the stated turns ratio.
• 120 V: Only a 10:1 step, not 20:1.
• 2,400 V: Off by a factor of 10; that would be a 200:1 ratio.

Common Pitfalls:
Mixing up the ratio as Np/Ns instead of Ns/Np, or assuming transformers change DC (they require AC to function properly).

Final Answer:
240 V