what is the equivalent circuit for battery in charging process?
A battery connected directly to the output of a solar panel will hold the solar panel's output at the battery voltage.  If you look at the I-V curve of a panel, you most likely will find that the maximum output power does not occur at the battery voltage.  This means that you will not be able to extract the maximum power from the panel.  Also, you wouldn't be able to control the charge profile of the battery, which can cause ill effects to the battery.  This is the reason for a device called a Maximum Power Point Tracker (MPPT), which you can google.  I know this doesn't answer the question asked in the post, but will hopefully help to set you in the right direction.