i guess that to calculate time constant in a capacitor, the formular is t=RC.
so when you connect a capacitor to a source, without a resisor with it, doesnt it still charge?, then why cos t=(0)*C =0. i might be missing something, any help is appreciated

 

It's true but there is never R=0. There is always some resistance.

 

i get it. does it mean it will then take a very long time to charge cos the resistance is very small?

 

No. Low resistance means quick responses.

Please be careful with cos(t) which means cosine of time
and "cos the resistance" which means "because the resistance".