Question

a capacitor is connected to a battery as shown..
C V
,---||-----|i----,
|________________|

work done by battery = Q . V

where Q is the net charge supplied by battery..
and V is potential difference across the terminals

energy stored by capacitor is (1/2)Q.V
V is potential difference at both plates.. (which should be equal to potential difference at the ends of battery, isn't it?)
and Q is charge on each plate of this parallel plate capacitor (which should be net charge provided by battery, isnt it?)

where did the rest of energy go?? i.e. (1/2)Q.V

Answer 1

that is stored in capcacitor

Answer 2

half is stored and the rest half??

Answer 3

there should be a resistor ..
if there is no resistor, then when the circuit is turned on, you might encounter short circuit.