Three initially uncharged capacitors are connected in series as shown in circuit with a battery of emf 30V. Find out following :
(i) charge flow through the battery,
(ii) potential energy in `3 mu F` capacitor.
(iii) `U_("total")` in capacitors
(iv) heat produced in the circuit

Explanation

` (1)/( C_(eq) )= (1)/(2)+ (1)/(3) +(1)/(6) =( 3+2+1)/( 6) =1 `
` C_(eq) =1 mu F . `
(i) ` Q=C_(eq) V= 30 muC`
(ii) charge on ` 3mu F ` capacitor = ` 30 mu C . `
energy ` = (Q^(2))/( 2C) =( 30xx 30)/( 2xx3) = 150 mu J`
(iii) ` U_('total") =( 30xx 30)/( 2) mu J = 450 mu J`
(iv) Heat produced ` = ( 30 mu C ) (30 ) - 450mu J = 450 mu J `