An uncharged capacitor is connected to a battery. Show that half the energy supplied by the battery is lost as heat while charging the capacitor.
Draw an equipotential surface for a uniform electric field. Can two equipotential surfaces intersect each other?

Can two equipotential surfaces cut each other?

If and uncharged capacitor is charged by connected it to a battery, then the amount of energy lost as heat is.

Prove that in charging a capacitor half of the energy supplied by the battery is stored in the capacitor and remaining half is lost during charging.

Assertion: When an uncharged capacitor is connected across a battery, half the work done by the battery is stored as electric potential energy inside the capacitor and remaining half is dissipated in the form of heat. Reason: When an uncharged capacitor is connected across the battery then potential difference between the plates of capacitor increases from zero to the value of EMF of battery but battery supplies charge at the constant potential difference.

Assertion : When an uncharged capacitor is charged by a battery only 50% of the energy supplied is stored in the capacitor. Reason : Rest 50% is lost.

If the capacitor is kept connected with the battery and then the dielectric slab is inserted between the plates, then what will be the change in the charge, the capacitance the potential difference, the electric field an the stored energy?