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Capacitors in Parallel Formula

We may connect several capacitors together in many applications. Multiple connections of capacitors will act as a single equivalent capacitor. The total capacitance of this equivalent single capacitor is depending both on the individual capacitors and also how they are connected. There are two simple and common types of connections that are possible, a series and parallel. For these, we can easily calculate the total capacitance. Some more complicated connections can also be related to combinations of series and parallel. In this article, let us discuss more the parallel configuration of capacitors. We will see the capacitors in parallel formula. Let us learn the concept!

capacitors in parallel formula

                                                                                                                                                              Source:  en.wikipedia.org

Capacitors in Parallel Formula

Concepts of Capacitors Connections

Multiple connections of capacitors are acting as a single equivalent capacitor. The total capacitance of this equivalent single capacitor will depend on the way of connections. There are many different ways of making connections. We may place the capacitors in parallel for many possible reasons. Some reasons are as follows:

  • Higher levels of capacitance
  • To provide an exact value which otherwise may not be available
  • To provide a distributed capacitance on a printed circuit board

Capacitors in Parallel Formula

We compute Total capacitance in parallel as,

\( C_{eq} = C_1 + C_2 + C_3 + C_4 + C_5 + …… \)

\(Where C_1, C_2,… are individual capacitors. \)

The total capacitance of a set of parallel capacitors is simply the sum of the capacitance values of the individual capacitors. Theoretically, there is no limit to the number of capacitors that can be connected in parallel. But certainly, there will be practical limits depending on the application, space and other physical limitations.

Applications of Parallel Capacitors

By combining several capacitors in parallel, the resultant circuit will be able to store more energy as the equivalent capacitance is the sum of individual capacitances of all capacitors involved. This effect is useful in the following applications.

  • DC power supplies are sometimes using parallel capacitors in order to better filter the output signal and eliminate the AC ripple.
  • Energy storage capacitor banks are useful for power factor correction with inductive loads.
  • Capacitive storage banks are useful in the automotive industry for regenerative braking in large vehicles such as trams and hybrid cars.

Using capacitors in parallel will provide additional flexibility in their use.

Solved Examples

Q.1: What total capacitances can you make by connecting a \(5.00 \muF and an 8.00 \muF\) capacitor together?

Solution: By applying the formula for a parallel combination we will get,

\(C_{eq} = 5 + 8 = 13.0 \muF\) in parallel combination.

Q.2: An 8.00 \(\muF\) capacitor is connected in parallel to another capacitor, producing a total capacitance of \(5.00 \muF\). What is the capacitance of the second capacitor? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Solution: (a) Applying the formula

\(C_{a} = C_{eq} – C_{b} \)

\(C_{a} = 5 – 8\)

\(C_{eq} =  –3.00 \muF \0

(b) We cannot have a negative value of capacitance.

(c) The assumption that the capacitors were hooked up in parallel, but it should be in series. It was incorrect. A parallel connection always produces a greater capacitance and not the smaller capacitance was assumed. This may happen only if the capacitors are connected in the series.

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