A step-down transformer changes the
potential difference of an alternating current from 10000 volts to 250 volts. If it has 25 turns on its secondary
coil, how many turns does it have on its primary coil?
Okay, let’s say that this is our
transformer. This is our primary coil and here
is our secondary coil. We’re told that the potential
difference in the primary coil, what we we’ll call 𝑉 sub p, is equal to 10000
volts. And the potential difference in the
secondary coil, what we’ll call 𝑉 sub s, is 250 volts. We’re also told that the secondary
coil of our transformer has 25 turns. We’ll call that number 𝑁 sub
s. And if we call the number of turns
in the primary coil 𝑁 sub p, it’s that value that we want to solve for. In order to do it, we can recall a
relationship between primary and secondary voltage and number of turns. This relationship says that the
ratio of the turns primary to secondary is equal to the ratio of potential
differences primary to secondary.
In this relationship, we want to
solve for 𝑁 sub p, the number of turns in the primary coil. So to do that, we can multiply both
sides of the equation by the number of turns in the secondary coil. That means that that term, 𝑁 sub
s, cancels out on the left-hand side of our equation. We find that 𝑁 sub p is equal to
𝑉 sub p divided by 𝑉 sub s all multiplied by 𝑁 sub s. And since we know 𝑁 sub s, 𝑉 sub
p, and 𝑉 sub s, we can substitute those values into this equation now. 𝑉 sub p is 10000 volts, 𝑉 sub s
is 250 volts, and 𝑁 sub s is 25. Calculating this result, we find an
answer of 1000. That’s the number of turns that are
in the primary coil of this transformer.