Astep up transformer has 350 turns on the primary coil and 1500 turns on the secondary coil the primary coil has a potential difference of 110 v across it, what is the power input and output of the transformer?

The power input and output of the transformer should be the same. That is exactly how we derive the transformer equations.

Explanation:

The main transformer equation relating the turn ratios, the voltages and the currents is as given below.

We got the third part of the equation by appreciating that input power and the output power of the transformer are equal. That is,

.

Using this fact exactly we get,

which we plug in the second equality of the first equation to obtain the third equality of the first equation. So the input and the output powers of the transformers are the same. If we were given a value for the input current we could have calculated the output current by using the first equation since we have available both turn ratios and then we could have used the third equation to calculate the power, where the secondary voltage is given by,

.

In actuality there are always some losses in the core of the transformer and due to the resistance and inductance of the wire making up the coil , due to which the output power would be somewhat less than the input power, but we need not concern ourselves too much with that since we cannot hope to calculate that because we don't have the relevant data available.