What happens if we put a load on both windings of a transformer? Suppose we have a transformer with equal number of spires on each winding. If we put a load on the secondary there will be no power on the primary, what happens if we put a load also on the primary? the secondary will get no power or  both will get half?
Can you explain why the secondary winding gets no power when there is a load on the primary? The primary current produces an oscillating MF in the core anyway, doesn't it? why does the secondary ged no power? putting a load on the primary does not prevent the winding from producing a MF, does it?
 A: Assuming the transformer is a one-to-one (equal number of turns on pri and sec) and the primary is connected to the mains supply, e.g. 230Vac, then: 


*

*The secondary will have close to 230Vac at it's output, whether it has a load connected to it or not (the load will actually cause a small drop in voltage but not much as long as the core is not saturating). 

*With no secondary load connected a very tiny current will flow in the secondary due to it's (very small) inherent capacitance. 

*If a load is connected to the secondary , the current flowing in the load will cause an equal current to flow in the primary. This is true whether or not there is also a load connected to (in parallel with) the primary. 

*The primary will draw some current (excitation current) from the mains even if no load is connected to the secondary. This current is made up of the magnetisation current (lags the voltage by 90 degrees) which produces the alternating magnetic field in the core, and the current due to core losses (eddy currents and hysteresis losses). 

*Connecting a load (e.g. an appliance) to the same power supply as the primary (i.e. in parallel with the primary) will not affect the primary or the secondary current of the transformer at all. This is true whether there is a secondary load or not.  

*The load (added in parallel with the primary) is supplied with current from the mains supply, whether the transformer is connected or not. It does not take any power from the transformer.  

*The only exception to this would be if the power supply is not very good and sags under the extra load, so that the voltage drops to less than 230V, the transformer would then get less voltage). 



"If we put a load on the secondary there will be no power on the
  primary"  

A load on the secondary draws power in the primary (as if the transformer was not there, if the windings are both the same and the windings are tightly magnetically linked).
If the power supply is good, loads connected to it in parallel draw power from the supply independently of each other.
I hope this answers your question.
