Analysis of transient state which occurs in electrical circuit if capacitors starts charging from voltage source. In considered example capacitor has collected initial electrical charge Q and thus it's charged with initial voltage.

 

Are you asking us to check your equations?

 

Analysis of transient state which occurs in electrical circuit if capacitors starts charging from voltage source. In considered example capacitor has collected initial electrical charge Q and thus it's charged with initial voltage.

Hello,

Is this a capacitor charging through a resistance? Sorry i can not read your pdf right now, but if you type it out here i can read it later.

If so, then the initial voltage of the capacitor changes the equation. It's as if the initial voltage subtracts from the source voltage. So the usual equation is:
Vc(t)=Vs*(1-e^(-t/RC))

and subtracting the initial cap voltage Vc0 from Vs we would have:
Vc(t)=(Vs-Vc0)*(1-e^(-t/RC))

but then we must add the initial voltage back again so we get:
Vc(t)=(Vs-Vc0)*(1-e^(-t/RC))+Vc0

This is the final equation, and if you plot that you'll see that the voltage rises exponentially just as it always does, except now instead of starting from zero it starts from the initial cap voltage and climbs up to the source voltage Vs exponentially as it did before. The change now is less however because the difference between Vs and Vc0 is less than the difference between Vs and zero.

The above equation simplified a little comes out to:
Vc(t)=Vs-(Vs-Vc0)*e^(-t/RC)