Question

What is the formula for calculating the capacitance of capacitors in parallel?

Answer 1

When capacitors are connected in parallel, the total capacitance \( C_{\text{total}} \) is simply the sum of the individual capacitances. The formula for calculating the total capacitance \( C_{\text{total}} \) of capacitors in parallel is:

\[ C_{\text{total}} = C_1 + C_2 + C_3 + \cdots + C_n \]

where \( C_1, C_2, C_3, \ldots, C_n \) are the capacitances of the individual capacitors.

### Explanation:
In a parallel configuration, each capacitor experiences the same voltage across it, and the total charge stored is the sum of the charges stored on each capacitor. Since capacitance is defined as \( C = \frac{Q}{V} \) (where \( Q \) is the charge and \( V \) is the voltage), if the voltage \( V \) is the same for each capacitor, the total charge \( Q_{\text{total}} \) is the sum of the charges on each capacitor. Thus, the total capacitance is the sum of the individual capacitances.

Answer 2

When capacitors are connected in parallel, the total or equivalent capacitance is simply the sum of the individual capacitances. This is due to the fact that each capacitor in parallel has the same voltage across it, and the total charge stored is the sum of the charges stored in each capacitor.

The formula for calculating the total capacitance \( C_{total} \) of capacitors connected in parallel is:

\[ C_{total} = C_1 + C_2 + C_3 + \ldots + C_n \]

where \( C_1, C_2, C_3, \ldots, C_n \) are the capacitances of the individual capacitors.

### Example

Suppose you have three capacitors with the following capacitances:

- \( C_1 = 4 \text{ µF} \)
- \( C_2 = 6 \text{ µF} \)
- \( C_3 = 10 \text{ µF} \)

To find the total capacitance:

\[ C_{total} = C_1 + C_2 + C_3 \]
\[ C_{total} = 4 \text{ µF} + 6 \text{ µF} + 10 \text{ µF} \]
\[ C_{total} = 20 \text{ µF} \]

Thus, the total capacitance of the three capacitors in parallel is 20 µF.