Video Transcript
A step-up transformer needs to
change the potential difference of an alternating current from 50 volts to 250
volts. If the transformer has 100 turns on
its primary coil, how many turns does it need to have on its secondary coil?
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. Here, weβve been told that the
input potential difference is 50 volts and that the output potential difference
needs to be 250 volts.
We can recall that the relationship
between the input and output potential difference depends upon the relationship
between the number of turns π 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.
Now, we already know values for
both the terms on the right-hand side of this expression. So we can write the ratio of π
input to π output as 50 volts divided by 250 volts, which just simplifies to
one-fifth, the units of volts canceling. Since this is equivalent to the
ratio of the turns in the primary to secondary coil, we know that π input divided
by π output equals one-fifth. Thus, the number of turns in the
primary coil needs to be one-fifth the number of turns in the secondary coil. We were told that the primary coil
has 100 turns. So, if this is one-fifth the number
of turns in the secondary coil, then in order for the relationship to hold true, the
secondary coil must have 500 turns. Therefore, the correct answer is
500 turns.
If the step-up transformer has 100
turns on its primary coil, then the secondary coil needs 500 turns in order to
change the potential difference of an alternating current from 50 volts to 250
volts.
