I have connected a dc motor and a dc fan to the a 12v 5a dc power supply.
both together draws a current of around 3A.When I remove motor from the circuit the fan speed is getting increased and if I reconnect the motor again speed of the fan getting reduced.Why this? can any one explain?
What can I do to avoid reduced speed of the fan when both connected together?

 

The supply internal resistance is causing the DC output voltage to drop at the higher current. At the lower DC voltage the fan speed is lower. It's an issue of poor regulation in the power supply.

 

Connect your voltmeter to the power supply output when you connect and disconnect the motor and you can very vividly see what TNK is describing to you. Both the fan and the motor are sensitive to their supply voltage. A very important concept to understand in electrical/electronics - circuit loading and internal resistance effects due to loading.