The 3A fuse in the heating and cooling unit keeps blowing. I have replaced the control board in the unit and it continued to blow. I ran new wire from the control board to the contractor, and it continues to blow. I disconnected the Thermostat wiring to the control board and jumed the R and the Y connectors to by pass the thermostat and the fuse blew. If it turn the unit off at the Thermostat the indicators lights come on and the fuse does not blow. I switched the unit to heating and the fuse blows. I am thinking my problem is with the transformer. Any helpful hints

I'm thinking you have a control wire short(s). If it does it on heat and cool cold be fan contactor coils shorted.
Remove wires from outside compressor contactor coil, if it blows on cool, it is likely control wiring to outside contactor.
Disconnecting wire to heat contactor will help determine if contactor or wiring, don't increase the size of the fuse.

The 3A fuse in the heating and cooling unit keeps blowing. I have replaced the control board in the unit and it continued to blow. I ran new wire from the control board to the contractor, and it continues to blow. I disconnected the Thermostat wiring to the control board and jumed the R and the Y connectors to by pass the thermostat and the fuse blew. If it turn the unit off at the Thermostat the indicators lights come on and the fuse does not blow. I switched the unit to heating and the fuse blows. I am thinking my problem is with the transformer. Any helpful hints
After more testing I found the Thermostate must have a short. And my control board was bad. It must have had a power surge or a storm whiel I was away from home. I disconnected the thermostate and joined the red and white and the heater worked and then joined the red and green wire to test the AC this also worked. Tomarow will purchase a new thermostat. I hope this may help someone else in the future.

When you jump from R to G that makes the blower run, If you jump from R to Y that's the compressor circuit. You may still have a short if that circuit was not tested.