### 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, weβre considering
a step-up transformer, meaning the transformer has an output potential difference,
which we call π output, that is greater than the input potential difference, π
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 transformerβs primary and secondary, or input and
output, coils. Specifically, we know that the
ratio of the number of turns π in the input and output coils is the same as the
ratio of the potential difference π across these coils. We can write this as π input
divided by π output equals π input divided by π 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 π input divided
by π output equals one-eighth, which we can then substitute into this equation. We also know that the input
potential difference, π input, equals 40 volts. So substituting this into the
equation, we get that one-eighth equals 40 volts divided by π output.

Since we want to solve for the
output potential difference, π output, letβs 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 π
output divided by 40 volts.

All thatβs left to do now is
multiply both sides by 40 volts, so that 40 volts term cancels out of the right-hand
side, leaving π output by itself. Thus, π 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.