A step-up transformer has a 20 V AC input and a 250 V output, with efficiency 90%. Its secondary feeds a 250 V, 100 W lamp. If the primary current is 50/x ampere, find x.
Physics · Mixed Chapter
JEE Mains

Question

A step-up transformer has a 20 V AC input and a 250 V output, with efficiency 90%. Its secondary feeds a 250 V, 100 W lamp. If the primary current is 50/x ampere, find x.

G1 Physics · Accepted Answer

Step 1 — Output power: The rated lamp takes P₂ = 100 W at 250 V. Step 2 — Apply transformer efficiency: η = P₂/P₁ = 0.90 ⇒ P₁ = 100/0.9 = 1000/9 W. Step 3 — Primary current: Iₚ = P₁/Vₚ = (1000/9)/20 = 50/9 A. Step 4 — Compare with Iₚ = 50/x: x = 9. Answer: 9.