A 100-percent efficient transformer has an input potential difference of 20 volts and an input current of four amps. If its output potential difference is 40 volts, what is its output current?
Okay, so in this question, we’ve got a transformer. And the first thing that we’re told about this transformer is that it’s 100 percent efficient. If anything is 100 percent efficient, then no energy is wasted. In other words, all of the energy put into a 100-percent efficient component comes out again as useful energy.
In other words, it’s not wasted as heat or sound or something like that. So in this case, we’ve got a 100-percent efficient transformer. Into a transformer, we put in electrical energy, because essentially what a transformer is is couple of coils around an iron core. Now the coils carry an electrical current, and so we put in electrical energy through the input coil.
And if it’s 100 percent efficient, then all of this energy comes out into the output coil as well, as electrical energy. So once again, this transformer is not wasting any of the energy as heat or it’s not humming and wasting the energy as sound or anything like that. Now this is a useful piece of information because we can recall that power is defined as the rate of transfer of energy, or energy transferred per unit time.
Now, in a 100-percent efficient transformer, we’ve said that no energy is wasted. Therefore, every second all of the energy that we put into the input coil comes out out of the output coil as well. So if the energy that goes in is equal to the energy that comes out, then naturally the energy that goes in per second must be equal to the energy that comes out per second as well.
Therefore, we can also make the following statement: the power that we put in is equal to the power that comes out. And the important thing is that we can relate this power to the potential difference and the current of the input and output coils. We can recall that power is given as potential difference multiplied by current.
Therefore, for the input coil, we can say that the input power is equal to the input potential difference multiplied by the input current. And we could say the same for the output power, which is equal to the output potential difference multiplied by the output current. But as we’ve said already, the input power is equal to the output power.
So we say that the input power is equal to the output power. Now at this point, we can see that in our question we’ve been given the values for the input potential difference, the input current, and the output potential difference. And we’ve been asked to find the output current. So we need to take this equation and rearrange it to find the output current.
We do this by dividing both sides of the equation by the output potential difference. This way the output potential difference cancels on the right-hand side, and we’re left with just the output current. This means we now have an expression for the output current.
The output current is equal to the input potential difference divided by the output potential difference, and we multiply this fraction by the input current. Now we have all of the quantities on the right-hand side of the equation given to us in the question. So we just need to sub in those values.
We say that the output current is equal to the input potential difference, 20 volts, divided by the output potential difference, 40 volts, multiplied by the input current, four amps. Evaluating this fraction then leads us to an answer of two amps. Hence, the output current of the transformer is two amps.