Circuit Connections in Capacitors

In a circuit, a Capacitor can be connected in series or in parallel fashion. If a set of capacitors were connected in a circuit, the type of capacitor connection deals with the voltage and current values in that network.

Capacitors in Series

Let us observe what happens, when few Capacitors are connected in Series. Let us consider three capacitors with different values, as shown in the figure below.

Capacitance

When the capacitance of a network whose capacitors are in series is considered, the reciprocal of the capacitances of all capacitors, is added to get the reciprocal of the total capacitance. To get this more clearly,

$$frac{1}{C_{T}}::=::frac{1}{C_{1}}::+::frac{1}{C_{2}}::+::frac{1}{C_{3}}$$

Following the same formula, if simply two capacitors are connected in series, then

$$C_{T}::=::frac{C_{1}:: imes::C_{2}}{C_{1}::+::C_{2}}$$

Where C₁ is the capacitance across the 1^st capacitor, C₂ is the capacitance across the 2^nd capacitor and C₃ is the capacitance across the 3^rd capacitor in the above network.

Voltage

The voltage across each capacitor depends upon the value of inspanidual capacitances. Which means

$$V_{C1}::=::frac{Q_{T}}{C_{1}}::V_{C2}::=::frac{Q_{T}}{C_{2}}::V_{C3}::=::frac{Q_{T}}{C_{3}}$$

The total voltage across the series capacitors circuit,

$$V_{T}::=::V_{C1}::+::V_{C2}::+::V_{C3}$$

Where V_c1 is the voltage across the 1^st capacitor, V_c2 is the voltage across the 2^nd capacitor and V_c3 is the voltage across the 3^rd capacitor in the above network.

Current

The total amount of Current that flows through a set of Capacitors connected in series is the same at all the points. Therefore the capacitors will store the same amount of charge regardless of their capacitance value.

Current through the network,

$$I::=::I_{1}::=::I_{2}::=::I_{3}$$

Where I₁ is the current through the 1^st capacitor, I₂ is the current through the 2^nd capacitor and I₃ is the current through the 3^rd capacitor in the above network.

As the current is same, the storage of charge is same because any plate of a capacitor gets its charge from the adjacent capacitor and hence capacitors in series will have the same charge.

$$Q_{T}::=::Q_{1}::=::Q_{2}::=::Q_{3}$$

Capacitors in Parallel

Let us observe what happens, when few capacitors are connected in Parallel. Let us consider three capacitors with different values, as shown in the figure below.

Capacitance

The total Capacitance of the circuit is the equivalent to the sum of the inspanidual capacitances of the capacitors in the network.

$$C_{T}::=::C_{1}::+::C_{2}::+::C_{3}$$

Where C₁ is the capacitance across the 1^st capacitor, C₂ is the capacitance across the 2^nd capacitor and C₃ is the capacitance across the 3^rd capacitor in the above network.

Voltage

The voltage measured at the end of the circuit is same as the voltage across all the capacitors that are connected in a parallel circuit.

$$V_{T}::=::V_{1}::=::V_{2}::=::V_{3}$$

Where V_c1 is the voltage across the 1^st capacitor, V_c2 is the voltage across the 2^nd capacitor and V_c3 is the voltage across the 3^rd capacitor in the above network.

Current

The total current flowing is equal to the sum of the currents flowing through each capacitor connected in the parallel network.

$$I_{T}::=::I_{1}::+::I_{2}::+::I_{3}$$

Where I₁ is the current through the 1^st capacitor, I₂ is the current through the 2^nd capacitor and I₃ is the current through the 3^rd capacitor in the above network.