Capacitors are devices that can store electric charge and energy in an electric circuit. They consist of two conductors, called plates, separated by an insulator, called a dielectric.
The amount of charge that a capacitor can store per unit of voltage is called its capacitance, and it is measured in farads (F)
Capacitors can be connected in different ways to form a combination of capacitors, which can have different effects on the total capacitance and the voltage distribution in the circuit.
The two most common types of connections are series and parallel, but they can also be combined to form more complex arrangements.
What is the equivalent capacitance Ceq of the entire combination?
In a series connection, the capacitors are connected end to end, so that the same charge flows through each capacitor. The total voltage across the combination is the sum of the voltages across each capacitor.The equivalent capacitance of a series combination is given by the formula:
Tegangan total pada kombinasi adalah jumlah tegangan pada masing-masing kapasitor. Kapasitansi ekivalen dari kombinasi seri diberikan dengan rumus:
where C1, C2, C3, … are the individual capacitances of the capacitors in the series. The equivalent capacitance of a series combination is always smaller than the smallest capacitance in the series
In a parallel connection, the capacitors are connected side by side, so that the same voltage is applied across each capacitor. The total charge on the combination is the sum of the charges on each capacitor. The equivalent capacitance of a parallel combination is given by the formula:
where C1, C2, C3, … are the individual capacitances of the capacitors in the parallel. The equivalent capacitance of a parallel combination is always larger than the largest capacitance in the paralle.
To find the equivalent capacitance of a more complex combination of capacitors, we can use the following steps:
- Identify the simplest sub-combinations of capacitors that are either in series or in parallel, and replace them with their equivalent capacitances.
- Repeat this process until the entire combination is reduced to a single equivalent capacitor.
- Use the formulas for series and parallel combinations to calculate the equivalent capacitance of each sub-combination along the way.
For example, consider the following combination of capacitors:
A combination of capacitors
We can start by identifying the sub-combination of C2 and C3, which are in parallel. We can replace them with their equivalent capacitance, which is C2 + C3.
Then, we can identify the sub-combination of C1 and C2 + C3, which are in series. We can replace them with their equivalent capacitance, which is 1 / (1 / C1 + 1 / (C2 + C3)).
Finally, we can identify the sub-combination of C4 and 1 / (1 / C1 + 1 / (C2 + C3)), which are in parallel. We can replace them with their equivalent capacitance, which is C4 + 1 / (1 / C1 + 1 / (C2 + C3)).
Using this method, we can find the equivalent capacitance of any combination of capacitors, as long as we can identify the series and parallel sub-combinations.
This can help us analyze the behavior of electric circuits that involve capacitors, and design circuits that have the desired capacitance and voltage characteristics.