# Capacitance - combining multiple capacitors for equivalent C

• MathewsMD
In summary, when calculating the equivalent capacitance of multiple capacitors in series, use Q=CV to get the dimension Farads. Additionally, Veq is equal to V1 + V2 + V3 + V4.
MathewsMD
Capacitance -- combining multiple capacitors for equivalent C

In the given problem, Ceq = C1C2C3C4/(C1 + C2 + C3 + C4)

The answer says the equivalent capacitance is always less than C1 but I can't come up with thy. When I do this, I can't seem to prove that equivalent capacitance is always less than C1. For example, if I let:

C1 = 998 F, C2 = 999 F, C3 = 1000 F and C4 = 10001 F, then I get an answer (767119326 F) and this is much larger than C1. Any suggestions?

(I realize the capacitances used here are very large, but they are just used to make a point.)

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Use Q=CV and discover that now four capacitors have to share the voltage that C1 would have had all on its own if C2,3,4 were absent!

Perhaps your formula is questionable ?
When I do
$${1\over C_{eq}} = {1\over C_1} + {1\over C_2} + {1\over C_3} + {1\over C_4}$$
I get something completely different ! Which has the right dimension. Your ##C_{eq}## does not have the dimension of Farads ...

Hint: The ##C_1 C_2 C_3 C_4## in the numerator is correct.

BvU said:
Use Q=CV and discover that now four capacitors have to share the voltage that C1 would have had all on its own if C2,3,4 were absent!

Hmmm...
Well I know:

Ceq = Q(V1 + V2 + V3 + V4)/(V1V2V3V4)

I just don't quite see how this shows Ceq < C1...do you mind explaining further?

You know this for two capacitors, because then it comes out right.
What you wrote here has the dimension Coulombs * Volts / Volts4 and that is not Farads ...
So: from where did you get this ?

You mean you know that
$${1\over C_{eq}} = {V\over Q} = {V_1\over Q}+{V_2\over Q}+{V_3\over Q}+{V_4\over Q}$$

1 person
BvU said:
You mean you know that
$${1\over C_{eq}} = {V\over Q} = {V_1\over Q}+{V_2\over Q}+{V_3\over Q}+{V_4\over Q}$$

Sorry, yes.

Ceq = Q/(V1 + V2 + V3 + V4)

Also, Veq = V1 + V2 + V3 + V4

So since C1 = Q/V1 then Ceq must be smaller (i.e. it is divided by more positive numbers).

Thank you!

Just in case you ever need to calculate the ##C_{eq}## for 4 capacitors in series: do you know how to work out
$${1\over C_{eq}} = {1\over C_1} + {1\over C_2} + {1\over C_3} + {1\over C_4}$$
to ## { C_{eq}} = {C_1 C_2 C_3 C_4 \over ?} ## ? And: can you guess why anyone would ever use capacitors in series in a circuit ?

## What is capacitance and how is it measured?

Capacitance is the ability of a material or system to store an electric charge. It is measured in units of Farads (F). One Farad is equal to one coulomb of charge per volt of potential difference. Capacitance can be calculated by dividing the charge stored by the potential difference across the system.

## What is the formula for calculating equivalent capacitance when combining multiple capacitors?

The formula for calculating equivalent capacitance when combining capacitors in series is: 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn. When combining capacitors in parallel, the formula is simply Ceq = C1 + C2 + C3 + ... + Cn.

## How does combining capacitors affect the overall capacitance?

Combining capacitors in series results in a smaller equivalent capacitance, while combining capacitors in parallel results in a larger equivalent capacitance. This is because in series, the potential difference is divided between the capacitors, reducing the overall charge storage. In parallel, the potential difference remains the same, but the total charge storage increases.

## What are some practical applications of combining capacitors for equivalent capacitance?

Combining capacitors for equivalent capacitance is commonly used in electronic circuits and devices. It allows for the creation of custom capacitance values by combining multiple capacitors. This is useful in filtering circuits, power supply circuits, and other electronic applications.

## What are some factors to consider when combining capacitors for equivalent capacitance?

When combining capacitors, it is important to consider their individual capacitance values, voltage ratings, and tolerance levels. It is also important to ensure that the capacitors are connected in the correct configuration (series or parallel) and that they are all functioning properly. Additionally, the overall capacitance and voltage rating of the combined capacitors should meet the requirements of the circuit or device.

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