Turns ratio application: A transformer has 110 V applied to the primary. If the turns ratio is 8 (secondary to primary), determine the secondary voltage.

Introduction / Context:
The turns ratio directly sets the voltage ratio for an ideal transformer. This problem checks comfort with scaling primary voltage to obtain the secondary voltage using the stated turns ratio convention.

Given Data / Assumptions:

• Primary voltage Vp = 110 V.
• Turns ratio is 8, interpreted as Ns/Np = 8.
• Ideal transformer: Vs/Vp = Ns/Np.

Concept / Approach:
Use the ideal relation Vs = Vp * (Ns/Np). A turns ratio greater than 1 implies a step-up in voltage on the secondary.

Step-by-Step Solution:
Ns/Np = 8Vs = Vp * (Ns/Np)Vs = 110 * 8 = 880 V

Verification / Alternative check:
Since the ratio is 8:1, the secondary voltage must be eight times the primary. The numeric result 880 V is consistent with a simple step-up.

Why Other Options Are Wrong:

• 8.8 V and 88 V: These would correspond to step-down scenarios or different ratio conventions.
• 8,800 V: Off by a factor of 10.

Common Pitfalls:
Misreading the direction of the turns ratio or mixing up primary and secondary positions in the ratio, which flips the result by a factor of 64 when squared for impedance or by 8 for voltage.

Final Answer:
880 V