Question

The ratio of the number of turns of the primary coil to the secondary coil of an ideal transformer is \( 5 : 1 \). The primary is connected to \( 220 \, V \) supply. What is the output power of the transformer if the output resistance is \( 11 \Omega \)?

• A. 1760 W
• B. 1100 W
• C. 176 W
• D. 100 W

Hint:

In an ideal transformer, power is conserved. First find secondary voltage using turns ratio, then apply Ohm’s law to get current and power.

Answer 1

The Correct Option is C

Step 1: Use transformer voltage relation.
For an ideal transformer:
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \]

Step 2: Substitute turns ratio.
Given \( N_p : N_s = 5:1 \), so:
\[ \frac{V_s}{220} = \frac{1}{5} \]

Step 3: Calculate secondary voltage.
\[ V_s = \frac{220}{5} = 44 \, V \]

Step 4: Use Ohm’s law for output current.
\[ I_s = \frac{V_s}{R} \]
\[ I_s = \frac{44}{11} = 4 \, A \]

Step 5: Calculate output power.
\[ P = V_s I_s \]
\[ P = 44 \times 4 \]

Step 6: Final calculation.
\[ P = 176 \, W \]

Step 7: Final Answer.
\[ \boxed{176 \, W} \]