Question

How can you calculate the equivalent capacitance of capacitors in series and parallel configurations?

Answer 1

To calculate the equivalent capacitance of capacitors in series and parallel configurations, you need to apply the following rules:

Capacitors in Series:
When capacitors are connected in series, their total capacitance (equivalent capacitance) is calculated as the reciprocal of the sum of the reciprocals of individual capacitances.

For N capacitors in series with capacitances C1, C2, C3, ..., CN, the equivalent capacitance (C_eq) is given by the formula:

1 / C_eq = 1 / C1 + 1 / C2 + 1 / C3 + ... + 1 / CN

Then, to find C_eq, take the reciprocal of both sides of the equation:

C_eq = 1 / (1 / C1 + 1 / C2 + 1 / C3 + ... + 1 / CN)

Capacitors in Parallel:
When capacitors are connected in parallel, their total capacitance (equivalent capacitance) is the sum of individual capacitances.

For N capacitors in parallel with capacitances C1, C2, C3, ..., CN, the equivalent capacitance (C_eq) is given by the formula:

C_eq = C1 + C2 + C3 + ... + CN

Note: The unit of capacitance is the Farad (F).

Example for Series Configuration:
Let's say you have three capacitors with capacitances 2μF, 3μF, and 4μF connected in series. To find their equivalent capacitance, use the formula:

1 / C_eq = 1 / 2μF + 1 / 3μF + 1 / 4μF

Now, calculate the sum on the right side of the equation:

1 / C_eq = 1 / 2μF + 1 / 3μF + 1 / 4μF = (6 + 4 + 3) / 12μF = 13 / 12μF

Finally, find C_eq by taking the reciprocal:

C_eq = 12μF / 13 ≈ 0.9231μF

Example for Parallel Configuration:
Let's say you have three capacitors with capacitances 2μF, 3μF, and 4μF connected in parallel. To find their equivalent capacitance, simply add the individual capacitances:

C_eq = 2μF + 3μF + 4μF = 9μF

So, the equivalent capacitance of the capacitors in parallel is 9μF.