Question

A power transmission line feeds input power at \(2200\,V\) to a step-down transformer with its primary windings having \(2000\) turns. The output power is delivered at \(220\,V\) by the transformer. If the current in the primary of the transformer is \(2\,A\) and its efficiency is \(80\%\), the output current would be:

• A. 32 A
• B. 8 A
• C. 16 A
• D. 4 A

Hint:

In transformers, power is conserved (approximately). For step-down transformers, voltage decreases while current increases.

Answer 1

The Correct Option is C

Step 1: Calculate input power.
\[ P_{\text{in}} = V_p \times I_p = 2200 \times 2 = 4400\,W \]

Step 2: Use efficiency relation.
\[ \eta = \frac{P_{\text{out}}}{P_{\text{in}}} \]
\[ 0.8 = \frac{P_{\text{out}}}{4400} \]

Step 3: Calculate output power.
\[ P_{\text{out}} = 0.8 \times 4400 = 3520\,W \]

Step 4: Use output power formula.
\[ P_{\text{out}} = V_s \times I_s \]
\[ 3520 = 220 \times I_s \]

Step 5: Solve for output current.
\[ I_s = \frac{3520}{220} \]
\[ I_s = 16\,A \]

Step 6: Interpretation.
Since voltage decreases, current increases in step-down transformer.

Step 7: Final conclusion.
\[ \boxed{16\,A} \]