if we have 2 capacitors connected in series, 1st one has charge q, and the other one is uncharged and a 5v battery connected across it with negligeble internal resistance, then what is the current flowing through each capacitor? also find the charge on each capacitor when the current is flowing through the circuit ?

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Solution

$L e t u s c o n s i d e r t h e c a p a c i \tan c e o f e a c h c a p a c i t o r i s C . W h e n t h e y a r e c o n n e c t e d i n s e r i e s t h i e r e q u i v a l e n t c a p a c i \tan c e = C / 2 . W h e n t h e y a r e c o n n e c t e d i n s e r i e s, c h a r g e q i s e q u a l l y s h a r e d a n d w h e n t h i s c o m b i n a t i o n i s c o n n e c t e d t o a b a t t e r y o f 5 V, t h e c h a r g e t h a t i s t a k e n b y t h i s c o m b i n a t i o n i s Q = \frac{5 C}{2} . N o w n e t c h a r g e t h a t w i l l b e f l o w i n g t h r o u g h t h e c a p a c i t o r s i s (Q - q) = (\frac{5 c}{2} - q) . T h r o u g h c a p a c i t o r c h a r g e s f l o w n o t c u r r e n t . c h a r g e o n e a c h c a p a c i t o r w h e n c u r r e n t i s f l o w i n g = 5 C / 4 .$

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