## Capacitors in Series – Class 12 | Chapter – 2 | Physics Short Notes Series PDF for NEET & JEE

Capacitors in Series: When capacitors are connected in series, they form a chain such that the positive terminal of one capacitor is connected to the negative terminal of the next capacitor. The total capacitance of a series combination of capacitors is given by:

1 / Ctotal = (1/C+ 1/C+…… + 1/Cn)

where Ctotal is the total capacitance of the combination and C1, C2, C3, …, Cn are the capacitances of the individual capacitors. The voltage across each capacitor in a series combination is divided among the capacitors.

## Capacitors in Series

In series combination of capacitors, the total capacitance is always less than the capacitance of any individual capacitor. The total capacitance decreases as the number of capacitors in the series combination increases. This is because the total capacitance of a series combination is inversely proportional to the sum of the reciprocals of the capacitances of the individual capacitors.

Series combination of capacitors is used in applications where a small total capacitance is required, such as in coupling and decoupling circuits, and in the creation of voltage dividers.

## Capacitors in Series Equation

When adding the series capacitors, the reciprocal ( 1/C ) of all the individual capacitors are added together ( just like the resistors in the parallel combination ) instead of capacitances themselves. The total value of the capacitors in the form of series combination equals the reciprocal of the sum of the reciprocal of their individual capacitances.

The total capacitance of a series combination of capacitors can be calculated using the following equation:

 Series capacitance 1 / Ctotal = (1/C1 + 1/C2 +…… + 1/Cn) Capacitors in Series Equation 1/Cr = 1/C1 + 1/C2 +…… etc

where Ctotal is the total capacitance of the combination, and C1, C2, C3, …, Cn are the capacitances of the individual capacitors.

In this equation, the total capacitance is inversely proportional to the sum of the reciprocals of the capacitances of the individual capacitors. As the number of capacitors in the series combination increases, the total capacitance decreases.

## Applications of Capacitors in Series

Capacitors in series are used in a variety of applications, including:

• Voltage Dividers: Capacitors in series can be used to create a voltage divider circuit, where a large voltage is divided into smaller, more manageable voltages.
• Coupling and Decoupling Circuits: Capacitors in series can be used to isolate or decouple different sections of a circuit, preventing the transfer of unwanted signals or noise between those sections.
• DC-DC Converters: Capacitors in series can be used in DC-DC converters to store and release energy as needed, allowing the conversion of one DC voltage level to another.
• Power Supplies: Capacitors in series can be used in power supply circuits to filter and smooth out the output voltage, removing any unwanted AC components and providing a stable DC voltage.
• Oscillators: Capacitors in series can be used in oscillator circuits to set the frequency of oscillation and determine the overall performance of the oscillator.
• Resonant Circuits: Capacitors in series can be used in resonant circuits to tune the resonant frequency of the circuit and to filter out unwanted frequencies.

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