Circuit Connections in Capacitors

# 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,

1CT=1C1+1C2+1C31CT=1C1+1C2+1C3

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

CT=C1Ã—C2C1+C2CT=C1Ã—C2C1+C2

Where C1Â is the capacitance across the 1stÂ capacitor, C2Â is the capacitance across the 2ndÂ capacitor and C3Â is the capacitance across the 3rdÂ capacitor in the above network.

### Voltage

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

VC1=QTC1VC2=QTC2VC3=QTC3VC1=QTC1VC2=QTC2VC3=QTC3

The total voltage across the series capacitors circuit,

VT=VC1+VC2+VC3VT=VC1+VC2+VC3

Where Vc1Â is the voltage across the 1stÂ capacitor, Vc2Â is the voltage across the 2ndÂ capacitor and Vc3Â is the voltage across the 3rdÂ 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=I1=I2=I3I=I1=I2=I3

Where I1Â is the current through the 1stÂ capacitor, I2Â is the current through the 2ndÂ capacitor and I3Â is the current through the 3rdÂ 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.

QT=Q1=Q2=Q3QT=Q1=Q2=Q3

## 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 individual capacitances of the capacitors in the network.

CT=C1+C2+C3CT=C1+C2+C3

Where C1Â is the capacitance across the 1stÂ capacitor, C2Â is the capacitance across the 2ndÂ capacitor and C3Â is the capacitance across the 3rdÂ capacitor in the above network.

### Voltage

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

VT=V1=V2=V3VT=V1=V2=V3

Where Vc1Â is the voltage across the 1stÂ capacitor, Vc2Â is the voltage across the 2ndÂ capacitor and Vc3Â is the voltage across the 3rdÂ 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.

IT=I1+I2+I3IT=I1+I2+I3

Where I1Â is the current through the 1stÂ capacitor, I2Â is the current through the 2ndÂ capacitor and I3Â is the current through the 3rdÂ capacitor in the above network.