The original circuit without the capacitor produced mostly heat in the battery and a little amount of light.
With the capacitor it produced mostly light and a little amount of heat.
The battery also lasted much longer with the capacitor.
For the duration of each 1400mA pulse with no capacitor, the battery is drained a lot. The battery will not get hot enough to damage itself.
I think that the high pulsed current with a duty cycle creating an average current of 300mA will reduce the life of the battery when compared to continuous 300mA.
thanks audioguru.it was an direct answer to my question.
so we can conclude that the battery with continuous 300mA will last longer than that with the high pulsed current one,whether it has a capacitor or not.but the high pulsed current one that will have capacitor will last longer than without capacitor.
thanks alot for all your replies.
and best regards