Physics Capacitors

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Capacitors

Capacitors in Series

In this arrangement charge has single path to flow, so charge will be same in each capacitor and equal to charge flown through
the battery

a) Charge on each capacitor are equal to

`i.e., Q = C_1V_1 = C_2V_2= C_3V_3`

b) The total potential difference across AB is shared by the capacitors in the inverse ratio of the capacitances

`V= V_1 +V_2 +V_3`

If `C_s` is the net capacitance of the series combination, then

`Q/C_s = Q/C_1 + Q/C_2 + Q/C_3`

`1/C_s = 1/C_1 + 1/C_2 + 1/C_3`

for n capacitors

`1/C_(equ) = 1/C_1 + 1/C_2 + 1/C_3 + ..........+ 1/C_n`

so in series combination equivalent capacitance is smaller than the smallest capacitance of the circuit.
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Capacitors in parallel

In parallel arrangement voltage difference will be the same across each capacitor and charge will divide in the ratio of capacitance.

a) The potential difference across each capacitor is same and equal the total potential applied.

`i.e., V = V_1 = V_2 = V_3`

`V= Q_1/C_1 = Q_2/C_2 = Q_3/C_3`

b) The total charge Q is sharped by each capacitors in the ratio of the capacity

`Q = Q_1 + Q_2 + Q_3`

If `C_p` is the net capacitance for the parallel combination of capacitors then

`C_p V = C_1V + C_2 V + C_3 V `

`C_p = C_1 + C_2 + C_3`

for n capacitor

`C_(equ) = C_1 + C_2 + C_3+ .............+ C_n`

so In parallel combination equivalent capacitance has greater value then greatest capacitance of circuit.