Question

A transformer connected to 220 V mains is used to light a lamp of rating 100 W and 110 V. If the primary current is 0.5 A, the efficiency of the transformer is (approximately)

• A. 60%
• B. 35%
• C. 50%
• D. 90%
• E. 44%

Hint:

Efficiency = Output/Input. Always compute actual power delivered, not rated voltage alone.

Answer 1

The Correct Option is D

Concept: Efficiency of transformer is defined as: \[ \eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100 \]

Step 1: Understand the given data carefully.

• Input voltage \(V_p = 220\,V\)
• Primary current \(I_p = 0.5\,A\)
• Lamp rating: \(100\,W\) at \(110\,V\)

Step 2: Determine output power.
Since the lamp is rated at 100 W and is operating properly at 110 V, the output power delivered by transformer is: \[ P_{\text{output}} = 100\,W \]

Step 3: Determine input power.
Input power is given by: \[ P_{\text{input}} = V_p \times I_p \] \[ P_{\text{input}} = 220 \times 0.5 = 110\,W \]

Step 4: Calculate efficiency.
\[ \eta = \frac{100}{110} \times 100 \]

Step 5: Simplify.
\[ \eta \approx 90.9% \approx 90% \]

Step 6: Final conclusion. \[ \boxed{90%} \]