Question

Derive the formula for the equivalent capacitance for a parallel combination of a number of Capacitors. plzzz give correct answer i need it for preparation of test

Answer 1

Answer:

In a parallel combination of capacitors, the capacitors are connected across a cell. Hence, the potential difference (V) across each each capacitor is the same. Let C1,C2,C3 be the capacitances of three capacitors connected in parallel and C be the equivalent capacitance of the combination.

Answer 2

Answer:

C=C1+C2+..+Cn

Explanation:

In a parallel combination of capacitors, the capacitors are connected across a cell. Hence, the potential difference (V) across each each capacitor is the same. Let C1,C2,C3 be the capacitances of three capacitors connected in parallel and C be the equivalent capacitance of the combination. The charge Q supplied by the cell is distributed as Q1,Q2andQ3 on the capacitors.

Since, capacitance =$\frac{charge}{potential difference}$

C1=Q1/V,     C2=Q2/V,     C3=Q3/V  and      C=Q/V  

∴Q1=C1V    ,Q2=C2V,     Q3=C3V    and      Q=CV

Now, Q=Q1+Q2+Q3

∴CV=C1V+C2V+C3V

∴C=C1+C2+C3

[Note: In general if n capacitors of capacitances C1,C2,...,Cn are connected in parallel, the equivalent capacitance of the equivalent capacitance of the combination is C=C1+C2+..+Cn]

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