Simple Series Circuits

In this article we will discuss about the series circuits. As we know that electronic circuits are the combination of passive and active components, which are different types and have different functionalities. We will focus mainly on the resistor based circuits that connected in series fashion.

What are Series Circuits..?

The connection of two terminal components in such a way that terminal 2 of first component is connected to terminal 1 of second component and terminal 2 of second component is connected to terminal 1 of third component and terminal 2 of third is connected to terminal 1 of fourth component and terminal 2 of fourth is connected to terminal 1 of first.

 

As shown in the above diagram, 9V battery is first component, R1 is second, R2 is third and R3 is fourth component. So in short the series connection is the one in which components are connected like Chain in closed loop fashion.

Example-1 of Series Connection:

The series circuit is the one in which same current flows through all the series component and the potential difference is dropped across each component according to its resistance values.

The terminal numbers are eliminated for sake of simplicity in the diagram on right.

The series circuit is the one in which each component carry equal current but different voltage is drop across each.

Here a 9V DC battery is connected in series with three series resistors R1 (3KΩ), R2 (10KΩ) and R3 (5KΩ).

Now we will find out the current and voltage values of each component and equivalent circuit current and resistance.

Current:

The current flow through each resistor connected in series is same and is equal to total equivalent current of series circuit. Therefore

It means that we have to find the total equivalent current of the circuit. So we have to find the equivalent resistance and then use Ohm’s Law to find total current.

Voltage:

The voltage across each resistor is found by applying “Voltage Divider Rule”

Voltage Divider Rule (VDR):

The voltage divider rule says that the sum of all the voltages across each series connected component is equal to the DC source voltage. Or “the sum of voltage drops is equal to sum of voltage rise.”

Where  in this example

Formula:

For three resistors connected in series as in our example. We have the formula for Voltage divider Rule

It means that, for the component whose voltage is desired its resistance is put in numerator and sum of all resistance is put in denominator then multiplied by source voltage

Series Equivalent Resistance:

The series equivalent resistance of two or more resistors connected in series is the sum of all the resistances in series.

Hence So we get

Series Equivalent Current:

Now we will find the series circuit total / equivalent current flow by applying Ohm’s Law

Now we can find the voltage across each resistor by applying Ohm’s Law again

Now when we add up all these voltage it becomes equal to 9V DC battery which approves VDR.

We can verify applying VDR:

Hence same results are proved.

 

Table:

R1 R2 R3
Resistance (R) 3KΩ 10KΩ 5KΩ
Voltage (V) 1.5V 5V 2.5V
Current (I) 0.5mA 0.5mA 0.5mA

 

Rule-1:

The equivalent resistance of the series combination of two or more than two resistors is always greater than the value of largest resistor in series.

Rule-2:

The equivalent resistance of two equal value resistors connected in series is double of that resistor value.

Rule-3:

In general, if “n” equal value resistors are connected in series, their equivalent resistance will be

 

Now back to the Example-1 of series circuit. We can represent the equivalent circuit by using single resistor as shown

Nodes:

As we can see that there are four junctions at which connection of terminals are made. The junctions highlighted with blue are nodes between components. Hence these component do not share single node instead there are different nodes for different terminal connections. In our example-1, we have 4 nodes as shown in diagram.

The Node 4 is connected to negative terminal of battery (Source) so it is called Ground Node (GND). Node4 is negative. While Node 1 is positive because it is connected to positive terminal of battery.

Other Examples of Series Circuits:

Series RLC Circuit:

Besides resistors, capacitors and inductors can also be connected in series combination to achieve desired functions. The series RLC circuit is widely used in resonant circuits, HPF, LPF, Band pass and stop filters and voltage multipliers

Batteries Connected in Series:

Multiple batteries can be connected in series to obtain a battery bank that meets the desired voltage ratings. For example you have load that operates are 9V and you have 1.5V AAA cell battery. So you need to connect these cells in series to attain 9V by adding voltage of each cells.

Inductors connected in Series:

The inductors connected in series will add up. The total inductance will be the sum of individual inductances.

Diode Clipper Circuit:

The diode can be connected in series with resistor to form a clipper circuit. This clipper circuit is used to clip the negative cycle in AC signals. Check the diagram below

 

Diode Clamper Circuit:

The diode connected in series with capacitor is called the clamper circuit. The clamper circuit is used to shift the AC signal to some offset voltage. This circuit basically adds a DC shift in the AC signal

 

Faults in Series Circuits:

Open Circuit:

If a component in a series combination of multiple components fails, that is becomes open circuit, then the current will stop to flow in the entire circuit and current flow through each component will become zero. The voltage across each component will also become zero.

Short Circuit:

If the component in a series combination of multiple components become short circuit, then the current in the circuit will continue to flow and each component carries equal current. But the voltage across that shorted component becomes zero and voltage across each component will depend upon its resistance value