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I was doing a question on transformers and found this really confusing question:

A 100% efficient transformer converts a 240V input voltage to a 12V output voltage. The output power of the transformer can be a maximum of 20W. The output is connected to two 0.30A bulbs in parallel. One of the bulbs fails. How does the current in the primary coil change?

What I did:

Since I have been given power and voltage I thought it would be helpful to figure out the current, so I did that which was fairly easy

20W/12V = 1.67 A

the output is connected to 2 0.3A bulbs so if one fails that's only 1 0.3A bulb

What I am stuck on

Now, this is where I kinda fall apart since I don't know where to go, I thought I would need to figure out some sort of ratio due to the transformer rule of the ratio of coil turns is equal to the ratio of voltages, but I don't really see where I would get information of the number of coils turns, however, my intuition is telling me that the current would increase...

Am I missing something that I haven't calculated from the question?

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    $\begingroup$ Hint: Since the transformer is 100% efficient, the power in the primary equals the power in the secondary. $\endgroup$
    – Bob D
    Commented Sep 2, 2020 at 14:08

2 Answers 2

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The 20 W is a maximum rating for the transformer and is of no concern unless it is exceeded. At 100% efficiency the power in equals the power out. In this case the power out (7.2 W) gets cut in half, so the current in (0.03 A) will also be cut in half.

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So the first thing we need to do is find the "step-down ratio". Due to how a transformer works, a small change in the secondary coil/output current will result in an even smaller change in the primary coil current.

  1. Ratio = $\frac{\text{Output Voltage}}{\text{Input Voltage}}$ = $\frac{12V}{240V}$ = $0.05A$

  2. Use the ratio to calculate the change in current in the primary coil. Because the bulbs are in parallel, the current will be shared equally to between each of them. So good news, we don't need to do anything fancy here - simply calculate the change of current if we lose one bulb.

    = $\frac{12V}{240V} \times 0.3A$

    = $0.015A$ decrease in the primary coil

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    $\begingroup$ Your ratio should have no units. $\endgroup$
    – R.W. Bird
    Commented Nov 26, 2020 at 14:39

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