Question

The ratio of the number of turns of the primary to the secondary coils in an ideal transformer is 20:1. If 240 V AC is applied from a source to the primary coil of the transformer and a 6.0 \( \Omega \) resistor is connected across the output terminals, then the current drawn by the transformer from the source will be:

• A. 4.0 A
• B. 3.8 A
• C. 0.97 A
• D. 0.10 A

Hint:

In transformers, the ratio of the primary to secondary voltage is equal to the ratio of the number of turns in the coils.

Answer 1

The Correct Option is D

For an ideal transformer, the relationship between the primary and secondary voltages is given by: \[ \frac{V_p}{V_s} = \frac{N_p}{N_s}, \] where \( V_p \) and \( V_s \) are the primary and secondary voltages, and \( N_p \) and \( N_s \) are the number of turns in the primary and secondary coils. Since the turns ratio is 20:1, the secondary voltage is: \[ V_s = \frac{V_p}{20} = \frac{240 \, \text{V}}{20} = 12 \, \text{V}. \] The current in the secondary is: \[ I_s = \frac{V_s}{R} = \frac{12 \, \text{V}}{6.0 \, \Omega} = 2.0 \, \text{A}. \] Using the turns ratio, the primary current is: \[ I_p = \frac{I_s}{20} = \frac{2.0 \, \text{A}}{20} = 0.1 \, \text{A}. \] Therefore, the current drawn by the transformer from the source is 0.1 A, corresponding to option (4).