Find the equivalent capacitance of capacitors Cand C2 connected in parallel.

Asked by Topperlearning User | 22nd Apr, 2015, 11:04: AM

Expert Answer:

In case of parallel arrangement, one end of all capacitors is attached to the same junction and the other end of all capacitors is connected to each other at another junction. The potential difference is the same across each of them.

 

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\epsfysize =2.5in
\centerline{\epsffile{cap1.eps}}
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The charge on each capacitor will not necessarily be the same if they have different capacitances because while the charging of the capacitors, the charges developed across the capacitor plates will be proportional to the capacitance of each capacitor since q=C V and V is the same for capacitors in parallel.

Now, for two capacitors in parallel, the total charge Q stored across an equivalent capacitor is divided between the two capacitors. Let the charges be Q1 and Q2
Thus

Q = Q1 + Q2
Then we can write

\begin{displaymath}
C_{\rm eq} = \frac{Q}{V} = \frac{Q_1+Q_2}{V} = \frac{Q_1}{V} + \frac{Q_2}{V},
\end{displaymath}

 

But  and since the potential difference or voltage V is the same across each capacitor.

\begin{displaymath}
C_{\rm eq} = C_1 + C_2.
\end{displaymath}

Hence, the equivalent capacitance of a set of capacitors in parallel is the sum of the individual capacitance.

Answered by  | 22nd Apr, 2015, 01:04: PM