**Parallel combination of capacitors**-Capacitors connected in parallel combination have same potential difference across their terminals shown below in fig

where

V=potential difference across terminals of capacitors c

_{1}, c

_{2}, c

_{3}

and Q

_{1}, Q

_{2}and Q

_{3}resp. are charges on capacitors c

_{1}, c

_{2}, c

_{3}.

-In parallel combination system of capacitors is equivalent to a single capacitor of capacitance

C=Q/V= C

_{1}+C

_{2}+C

_{3}

where, C

_{1}=Q

_{1}/V

C

_{2}=Q

_{2}/V

C

_{3}=Q

_{3}/V

-Thus for capacitors connected in parallel combination their resultant capacitance C is the sum of their individual capacitances.

-Also for parallel combination of capacitors their resultant capacitance C is greater then the capacitance of greatest individual one.

(b)

**Series combination of capacitors**

-Figure above shows three capacitors connected in series combination

-In series combination of capacitors potential difference across each capacitor is different but charge on each capacitor is same.

-The resultant capacitance of capacitors connected in series combination is the ratio of charge stored to the applied potential difference V and is given by

C=Q/V

or 1/C=V/Q

now V=V

_{1}+V

_{2}+V

_{3}

=Q(1/C

_{1}+1/C

_{2}+1/C

_{3})

Thus,

1/C=1/C

_{1}+1/C

_{2}+1/C

_{3}

-Resultant capacitance Cof the capacitors connected in series combination is equal to the sum of reciprocals of their individual capacitances. Here in case of series combination C is less then the capacitance of smallest individual capacitor.

(c)

**Energy stored in capacitor**-Energy stored in capacitor is

E=QV/2

or E=CV

^{2}/2

or E=Q

^{2}/2C

factor 1/2 is due to average potential difference across the capacitor while it is charged.

-Battery supply QV amount of energy during charging a capacitor but energy stored in capacitor is QV/2 , the another half of energy is transferred into the circuit resistance in the form of heat.

thus,

heat in the wire=energy supplied by battery-energy stored in the capacitor

=QV-QV/2 = QV/2

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