A transformer has 200 turns on its primary coil and 50 turns on its secondary coil. If the input potential difference is 20 volts, what is the output potential difference?
Okay, so in this question, we’re dealing with a transformer which we’ve been told has 200 turns on its primary coil. So we can say that 𝑛 𝑝, the number of turns on the primary coil, is 200. And we also know that it has 50 turns on its secondary coil. In other words, the number of turns 𝑛 sub 𝑠 on the secondary coil is 50.
As well as this, we know the input potential difference or in other words the potential difference across the primary coil which we’ll call 𝑉 sub 𝑝 and we know that it’s 20 volts. this is because the primary coil is on the input side of the transformer and the secondary coil is on the output side. Hence, the potential difference across the primary coil is the same thing as the input potential difference. And in this question, we need to find the output potential difference, which in other words is the potential difference across the secondary coil, 𝑉 sub 𝑠.
Now, to find 𝑉 sub 𝑠, we can recall that for a transformer the turns ratio 𝑛 sub 𝑠 over 𝑛 sub 𝑝 or in other words the number of turns on the secondary coil divided by the number of turns on the primary coil is equal to the voltage ratio of the same coils, in other words the output voltage divided by the input voltage or the voltage across the secondary coil divided by the voltage across the primary coil.
So we can use this equation to rearrange and solve for the output potential difference. We can do this by multiplying both sides of the equation by 𝑉 𝑝, the potential difference across the primary coil. This way, 𝑉 𝑝 cancels on the right-hand side. And what we’re left with is that 𝑉 𝑝 multiplied by 𝑛 𝑠 over 𝑛 𝑝, the turns ratio, is equal to 𝑉 𝑠. Then we can plug in the values for 𝑉 𝑝, 𝑛 𝑠, and 𝑛 𝑝. So we have 20 volts as 𝑉 𝑝 multiplied by 50, that’s 𝑛 𝑠, divided by 200, that’s 𝑛 𝑝. And then, when we evaluate the left-hand side of the equation, we find that 𝑉 sub 𝑠 is equal to five volts.
In other words, the output potential difference for this transformer is five volts.