I am using hp pavillion notebok with windows and ubuntu dual boot, whenver i shutdown my laptop and start the ubuntu after some time, i founds that the charging is reduced very much. I have tried the hp's utility for checking wethter battery is working fine or not and the utility says that it is working fine, so where it the problem
You probably have laptop which uses optimus technology. The idea behind optimus is that you have a weaker Intel based graphics card which will be used by standard applications that do not require much 3d power and an Nvidia graphics card which should be used by games, rendering software etc... Using this setup allows your laptop to benefit from increased battery life as well as good performance when required.
Unfortunately, Nvidia has not shown much support for this technology on linux and as a result your Nvidia discrete chip will be turned on at all times when you are running Ubuntu. This results in much more power being used and why your battery is draining so fast.
In order to fix this, you can install bumblebee which will provide you with the power management required to give you a much longer battery life and the appropriate tools to run applications using the Nvidia chip when required.
As far as i know, the only thing bumblebee is currently missing is: * Automatic detection of when to run the nvidia chip (currently this has to be done manually by using the optirun or primusrun command) * HDMI out support if it is wired to your NVidia chip.
Of course, this is all under the assumption that you are using an HP laptop that uses optimus technology - so you will need to check yourself with a bit of googling.
EDIT: It is also possible to have hybrid technology with ATI graphics cards. I believe bumblebee still provides support for this - but i am not sure how well it does it.