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Obtain an expression for the capacitance of a combination of three capacitors in parallel . |
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Answer» Solution :Let three capacitors of a capacitances `C_1 , C_2` and `C_3` ,respectively are JOINED in parallel such that one plate of all the three capacitors has been joined at one point A and the other plates are another point B . Here potential difference across all the three capacitors is same (say V) and charges on different capacitors are `Q_(1) = C _(1) V , Q_(2)= C_(2) V` and `Q_(3) = C_(3) V` Total charge on all the three capacitors TAKEN together `Q = Q_(1) + Q_(2) + Q_(3) = C_(1) V + C_2 V + C_3 V` If a single capacitor of CAPACITANCE C is joined instead of given capacitors such that the potential difference across it still remains V , then Q = CV `CV = C_1 V + C_2 V + C_3 V` `implies` RESULTANT capacitance `C = C_1 + C_2 + C_3` 
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