Electronic – Inductor in transformer

The fluxes created by the primary and the secondary windings are not equal; your equotion \$\frac{V_1}{V_2}=\frac{N_1}{N_2}\$ is just an approximation.

If you connect a transformer to the mains, but not to the load, the current flowing through the primary winding will create some flux in the core. It's determined by mains voltage, frequency and primary winding inductance. If you connect a load to the transformer, the primary current will increase in a way to keep the core flux close to what it was without load.

An 'ideal' transformer has its primary inductance rising up to infinity, so the unloaded (magnetizing) primary current drops down to zero. But infinite inductance multiplied by infinitely small current results in some definite flux in the core.

I have read that for transformers operating at low frequencies, a larger core is needed.

Correct when comparing to a transformer operating at a higher frequency but with the same line voltage. This is because of core saturation problems. Generally, a 240 V AC 50 Hz transformer run at 5 Hz should not have more than 24 V AC applied to it (for example).

I thought this formula for finding the induced voltage in the secondary coil would apply

The voltage induced on the secondary is related to the ratio of the turns between primary and secondary with a couple of provisos: -

1. Primary leakage components (such as copper loss) is not significant enough to "drop" much voltage. Any vot drop here results in a lowering of the voltage actually applied to the "useful" turns in the primary.
2. The coupling between primary and secondary is near 100%. Loss of coupling means loss of secondary voltage and increased leakage components on secondary and this has more of an effect under load conditions.

Is this the correct formula to use?

No, you need to take account of the turns ratio and the other points mentioned above.

If the above formula gives me a value for the induced voltage in the secondary coil that equals a lower Watts value in the secondary coil than in the primary coil, does this mean that the transformer core is too small for the frequency?

It can also mean that copper losses are significant. It can also mean that eddy current losses are significant. It can mean that coupling is not great and yes, it can also mean the core might be saturating.