Question

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

Answer 1

`(1)/(C_(eq))=(1)/(2)+(1)/(3)+(1)/(6)=(3+2+1)/(6)=1`
`C_(eq)=1mu F`.
(i)`Q=C_(eq) V=30mu C`.
(i) charge on `3mu F` capacitor `=30mu C`
energy `=(Q^(2))/(2C)=(30xx30)/(2xx3)=150mu J`
(iii)` U_("total")=(30xx30)/(2) mu J = 450 mu J`
(iv) Heat produced `=(3 mu C)(30)-450 mu J=450 mu J`.