if capacitor is connecteted to battery, and dielectric is inserted. what will happen with electric field inside capacitor?

I think it would not change because potential difference is constant and the distance bw plates is same........

charge will be K times the initial charge, in order to keep the electric field same................

when dielectric is inserted the electric field in the dielectric is opposite direction to the out side electric field so the electric field decreases as E_t=E_c-E_di.

But thats the case when capacitor is isolated (Not connected to battery................)