Question Video: Finding the Output Potential Difference of a Transformer | Nagwa Question Video: Finding the Output Potential Difference of a Transformer | Nagwa

Question Video: Finding the Output Potential Difference of a Transformer Physics • Third Year of Secondary School

A step-up transformer has 8 times as many turns on its secondary coil as it does on its primary coil. If its input potential difference is 40 V, what is its output potential difference?

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Video Transcript

A step-up transformer has eight times as many turns on its secondary coil as it does on its primary coil. If its input potential difference is 40 volts, what is its output potential difference?

In this question, we’re considering a step-up transformer, meaning the transformer has an output potential difference, which we call 𝑉 output, that is greater than the input potential difference, 𝑉 input.

We can recall that the relationship between the input and output potential difference depends upon the relationship between the number of turns in the transformer’s primary and secondary, or input and output, coils. Specifically, we know that the ratio of the number of turns 𝑁 in the input and output coils is the same as the ratio of the potential difference 𝑉 across these coils. We can write this as 𝑁 input divided by 𝑁 output equals 𝑉 input divided by 𝑉 output.

Here, we were told that the step-up transformer has eight times as many turns on its secondary coil as it does on its primary coil. So this means that 𝑁 input divided by 𝑁 output equals one-eighth, which we can then substitute into this equation. We also know that the input potential difference, 𝑉 input, equals 40 volts. So substituting this into the equation, we get that one-eighth equals 40 volts divided by 𝑉 output.

Since we want to solve for the output potential difference, 𝑉 output, let’s rearrange this expression to make that term the subject. We can start by taking the reciprocal of both sides of the equation. So it now reads, eight equals 𝑉 output divided by 40 volts.

All that’s left to do now is multiply both sides by 40 volts, so that 40 volts term cancels out of the right-hand side, leaving 𝑉 output by itself. Thus, 𝑉 output equals 40 volts times eight, which comes out to 320 volts. This is the correct answer. If this step-up transformer has an input potential difference of 40 volts, then its output potential difference will be equal to 320 volts.

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