## Capacitor Series and parallel Calculation:

Capacitor is a passive component used to remove unwanted voltage clips from the circuit. The multiple connections of multiple capacitors are used to filter the high voltage circuit. They can be connected in series or parallel.

### Capacitor in Series Formula:

The series connected capacitor’s equivalent capacitance C_{(equ)} in farad is equal to the inverse sum of the individual capacitance in farad. The series formula can be written as,

1/C_{(equ)} = 1/C_{1} + 1/C_{2} + 1/C_{3} + ……….+ 1/C_{n}

Let us consider as two series capacitor circuit and the applied voltage of V. here the V1 and V2 are the voltage drop across the capacitor. According to the Kirchhoff voltage rule, The algebraic sum of the individual capacitor voltage drop is equal to the applied voltage. Hence

V = V1 + V2

As you know, the voltage drop across the capacitor is equal to the product of the current in amps and the capacitive reactance Xc in amps

I*Xc = I* X_{c1} + I * X_{c2}

From above,

Xc = Xc1 + Xc2

Apply the capacitive reactance is equal to the one divided by 6.28 times of the capacitance and the input frequency.

1/6.28* f * C_{equ} = 1/6.28 * f * C_{1} + 1/6.28 * f * C_{2}

1/C_{equ} = 1/C_{1} + 1/C_{2}

Hence the series-connected capacitor will be,

C_{equ} = C_{1} * C_{2} / C_{1} + C_{2}

### Capacitor Connected in Parallel Connection:

The equivalent capacitance of a parallel-connected capacitor is equal to the algebraic sum of all parallel connected capacitor.

C_{equ} = C_{1} + C_{2} +……….+ C_{N}

Let us consider the two capacitors C1 and C2 are connected in parallel to a voltage source V. The current flowing through the capacitor is I1, I2 and I is the current flowing through the total circuit.

Here apply current law, @ node A the sum of incoming current is equal to the outgoing to current.

Hence,

I = I_{1} + I_{2}

Apply ohms law,

V/Xequ = V/Xc1 + V / Xc2

1/X_{equ} = 1/Xc1 + 1/Xc2

Sub X = 1 / 6.28 *f * C

Hence,

C_{equ} = C_{1} + C_{2}

Like that when you connect the N number of the capacitor, The equivalent capacitance will be,

C_{equ} = C_{1} + C_{2} + …….+ C_{N}

__Example:__

Let us calculate the equivalent capacitance of 25 micro fards and 12 microfarad capacitor is connected in series with each other.

1 / Cequ = 1 / 0.000025 + 1/ 0.000012

Cequ = 8.1 microfarad

__Example2:__

Calculate the total equivalent capacitance of three capacitors such as 10 microfarads, 15 microfarad, and 25 microfarads is connected in parallel.

As per the above calculation,

The parallel-connected capacitor’s equivalent capacitance Cequ = C1 + C2 + C3.

= 10 + 15 + 25 micro farad.

= 50 micro farad.