Question

A 12V, 60W lamp is connected to the secondary of a step down transformer, whose primary is connected to ac mains of 220V. Assuming the transformer to be ideal, what is the current in the primary winding?

• A. 0.37 A
• B. 0.27 A
• C. 2.7 A
• D. 3.7 A

Answer 1

The Correct Option is B

To determine the current in the primary winding of the transformer, we need to use the principles of an ideal transformer. Here are the steps to solve the problem:

1. Understanding the given data:
   • The secondary voltage \(V_s = 12\text{V}\).
   • The power of the lamp \(P = 60\text{W}\).
   • The primary voltage \(V_p = 220\text{V}\).
2. Find the current in the secondary winding:
   The power consumed by the lamp can be used to find the current in the secondary winding using the formula: \(I_s = \frac{P}{V_s}\)
   • Substituting the known values:
     \(I_s = \frac{60}{12} = 5\text{A}\)
3. Using the ideal transformer equation:
   An ideal transformer maintains the relationship between the primary and secondary voltages and currents as:
   \(\frac{V_p}{V_s} = \frac{I_s}{I_p}\)
   • We can rearrange this equation to find the primary current:
     \(I_p = \frac{V_s \cdot I_s}{V_p}\)
   • Substitute the values to get:
     \(I_p = \frac{12 \cdot 5}{220} \approx 0.27\text{A}\)
4. Conclusion:
   The current through the primary winding of the transformer is approximately 0.27 A. Thus, the correct answer is 0.27 A.
   The reason the other choices are incorrect is because they do not satisfy the mathematical relationship in an ideal transformer when calculated correctly.

This solution follows the principles of physics for an ideal transformer and applies the correct formulae to arrive at the answer.