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!

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.

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
Ashhar Firdausi
IIT Roorkee
Biology
Dr. Nazma Shaik
VTU
Chemistry
Gaurav Tiwari
APJAKTU
Physics
Get Started

7 Followers

Most reacted comment
5 Comment authors
Recent comment authors
Subscribe
Notify of
Guest

Typo Error>
Speed of Light, C = 299,792,458 m/s in vacuum
So U s/b C = 3 x 10^8 m/s
Not that C = 3 x 108 m/s
to imply C = 324 m/s
A bullet is faster than 324m/s

Guest

I have realy intrested to to this topic

Guest
umer

m=f/a correct this

Guest
B. Akshaya

M=f/g

Guest

Interesting studies

Guest
Yashdeep tiwari

It is already correct f= ma by second newton formula…

Question Mark?

Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps.