# Electronics Toolbox

## Series Capacitance Calculator

This tool calculates the capacitance of capacitors in series.

Capacitor 1
Capacitor 2

### Understanding Capacitors in Series

When capacitors are connected in series, the effective capacitance decreases. This happens because the charge $$Q$$ across each capacitor remains the same, but the voltage across each adds up, resulting in a lower overall capacitance compared to any single capacitor in the series.

#### How to Calculate

The formula to find the total capacitance $$C_{\text{total}}$$ of capacitors in series is given by the reciprocal of the sum of the reciprocals of each individual capacitor's capacitance:

##### $$\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \dots + \frac{1}{C_n}$$

where:

$$C_1, C_2, C_3, \dots, C_n$$ are the capacitances of each individual capacitor in the series.

#### Example

Suppose you have three capacitors in series with capacitances of 4 µF, 6 µF, and 12 µF. To find the total capacitance, use the formula:

##### $$\frac{1}{C_{\text{total}}} = \frac{1}{4\, \mu F} + \frac{1}{6\, \mu F} + \frac{1}{12\, \mu F}$$

Calculating this, we find:

##### $$\frac{1}{C_{\text{total}}} = 0.25\, \mu F^{-1} + 0.1667\, \mu F^{-1} + 0.0833\, \mu F^{-1} = 0.5\, \mu F^{-1}$$

So, the total capacitance $$C_{\text{total}}$$ is:

#### Visual Representation

Visualizing this in a circuit:

Imagine each capacitor connected end-to-end (like a daisy chain). The first plate of the first capacitor connects to the second plate of the second capacitor, and so on, with the outer plates connecting to the circuit.

#### Key Points

• Total Capacitance Decreases: In series, the total capacitance is always less than the smallest individual capacitor's capacitance in the group.
• Voltage Adds Up: The voltage across each capacitor when in series adds up, which is why the overall capacitance decreases.