Transformer efficiency calculation: A 120 V rms primary draws 300 mA rms. The secondary supplies 18 V across a 10 Ω load. Compute the efficiency η = P_out / P_in.

Introduction / Context:Transformer efficiency quantifies how effectively input power is converted to useful output power. Real transformers exhibit copper losses (I^2R), core losses (hysteresis and eddy currents), and stray losses. A quick efficiency check validates design sizing and reveals abnormal loading or faults.

Given Data / Assumptions:

• Primary voltage V_p = 120 V rms.
• Primary current I_p = 0.300 A rms.
• Secondary voltage V_s = 18 V rms across R_L = 10 Ω.
• Assume sinusoidal steady state and that meter readings are true rms.

Concept / Approach:Compute input power P_in = V_p * I_p (power factor assumed near unity for simplicity; many small transformers under resistive loading are close). Compute output power P_out = V_s^2 / R_L. Efficiency η = P_out / P_in expressed as a percentage.

Step-by-Step Solution:

Verification / Alternative check:Secondary current I_s = V_s / R_L = 18 / 10 = 1.8 A. If the turns ratio were measured, P_out should still be near 32.4 W; any large discrepancy from 36 W input indicates realistic losses yielding efficiency below 100%.

Why Other Options Are Wrong:

• 88% / 92% / 95%: Close but inconsistent with the direct calculation; only 90% matches P_out and P_in.

Common Pitfalls:Multiplying V and I on the secondary without considering the load, or forgetting to square V when using P = V^2 / R; also, mixing rms and peak values leads to errors.

Final Answer:90%