Question

An AC source of internal resistance \( 10^3 \ \Omega \) is connected to a transformer. The ratio of the number of turns in the primary to the number of turns in the secondary to match the source to a load resistance of \( 10 \ \Omega \) is

• A. \( 1 : 10 \)
• B. \( 10 : 1 \)
• C. \( 2 : 5 \)
• D. \( 5 : 2 \)

Hint:

Use the transformer impedance matching rule \( \left( \frac{N_p}{N_s} \right)^2 = \frac{R_s}{R_L} \) to optimize power transfer.

Answer 1

The Correct Option is B

Step 1: Matching load using transformer turns ratio
Impedance matching condition for transformers: \[ \frac{R_s}{R_L} = \left( \frac{N_p}{N_s} \right)^2 \] where \( R_s = 10^3 \ \Omega \), \( R_L = 10 \ \Omega \) Step 2: Taking square root on both sides
\[ \frac{N_p}{N_s} = \sqrt{\frac{10^3}{10}} = \sqrt{100} = 10 \] Step 3: Final Answer
Hence, the required ratio of primary to secondary turns is \( 10:1 \)