Video: Finding the Input Potential Difference of a Transformer

A transformer has 300 turns on its primary coil and 150 turns on its secondary coil. If the output potential difference is 100 V, what is the input potential difference?

02:16

Video Transcript

A transformer has 300 turns on its primary coil and 150 turns on its secondary coil. If the output potential difference is 100 volts, what is the input potential difference?

Okay, so in this question, we’ve been told that we have a transformer which has 300 turns on its primary coil and 150 turns on its secondary coil. We’ve been given the output potential difference, which is 100 volts, and we need to find the input potential difference. To do this, we need to recall the following equation.

On the left-hand side, we have the ratio between the number of turns on the primary coil, 𝑁 sub 𝑃, and the number of turns on the secondary coil, 𝑁 sub 𝑆. On the right-hand side, we have the potential difference in the primary coil, 𝑉 sub 𝑃, divided by the potential difference in the secondary coil, 𝑉 sub 𝑆.

Now, in the question, we’ve already been given the number of turns on the primary coil, the number of turns on the secondary coil, and the output potential difference. What we need to do is to work out the input potential difference. But hang on a minute! Didn’t we say that these were the potential differences in the primary and secondary coil? Well, how do we know which one is the input potential difference and which one’s the output potential difference?

We know this because the primary coil is defined as having the input potential difference, and the secondary coil has the output potential difference. In a transformer, a current comes into the primary coil and another current is generated in the secondary coil, which then leaves the transformer. Hence, the input potential difference is the potential difference of the primary coil, and the output potential difference is the potential difference of the secondary coil.

So we need to rearrange this equation to solve for 𝑉 sub 𝑃. We do this by multiplying both sides of the equation by 𝑉 sub 𝑆. When we do this, we find that 𝑉 sub 𝑆 multiplied by 𝑁 sub 𝑃 over 𝑁 sub 𝑆 is equal to 𝑉 sub 𝑃. We’re trying to find the value of 𝑉 sub 𝑃. And as we’ve already said, we’ve got the values of 𝑉 sub 𝑆, 𝑁 sub 𝑃, and 𝑁 sub 𝑆. So we need to plug them in.

So we say that 𝑉 sub 𝑆, which is 100 volts, multiplied by 𝑁 sub 𝑃, which is 300, divided by 𝑁 sub 𝑆, which is 150, is equal to 𝑉 sub 𝑃. Evaluating the fraction on the left-hand side then, we find that 𝑉 sub 𝑃 is equal to 200 volts. But remember, we already said that the potential difference in the primary coil is the same as the input potential difference. So this is the answer that we’re looking for. And hence, our final answer is that the input potential difference is 200 volts.

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