Question 449: AC fundamentals

Question

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

Accepted Answer

To find the current in the primary winding of an ideal step-down transformer, we first understand that an ideal transformer's power input (primary side) equals its power output (secondary side). This is because an ideal transformer is assumed to have 100% efficiency, meaning there are no losses in the transformation process.
The power of the lamp (which is connected to the secondary side of the transformer) is given as $$60\,\mathrm{W}$$, and it operates at $$12\,\mathrm{V}$$. The voltage on the primary side of the transformer is $$220\,\mathrm{V}$$.
Using the power formula $$P = IV$$, where $$P$$ is the power in watts, $$I$$ is the current in amperes, and $$V$$ is the voltage in volts, we equate the power on both sides of the transformer because of its ideal nature, i.e., $$P_{	ext{primary}} = P_{	ext{secondary}}$$.
Hence, $$60\,\mathrm{W} = 220\,\mathrm{V} 	imes I_{	ext{primary}}$$.
Solving for $$I_{	ext{primary}}$$ gives:
$$I_{	ext{primary}} = \frac{60\,\mathrm{W}}{220\,\mathrm{V}} = 0.2727... \approx 0.27\,\mathrm{A}$$.
Therefore, the current in the primary winding of the transformer is approximately $$0.27\,\mathrm{A}$$.

Answer

2.7 A

Answer

3.7 A

Answer

0.37 A

Answer

0.27 A

AC fundamentals

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

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