## What are Resistors in Series : Working & Its Applications

A resistor is a two-terminal passive electrical and electronic component, used to reduce the flow of current & lower voltage levels in different circuits. In most electrical and electronic circuits, there are more than one resistor is used to restrict the current flow in a circuit by connecting in different combinations like resistors in series or parallel or in both the combinations of series & parallel to form more complex resistor networks. The whole resistance of resistors mainly depends on their connections & individual values. This article discusses an overview of resistors in series, working with applications.

### What are Resistors in Series?

The definition for resistors in series is when resistors in a circuit are connected in sequence, then the flow of current throughout every resistor will be the same. And the potential difference or total voltage across all the connected resistors is equivalent to the addition of the voltages across every resistor. So, the sum of flow of current throughout a set of resistors within a series connection is the same at everyone point in a series connection of a network. The resistor in the series symbol is shown below.

### Resistors in Series Circuit Diagram

The circuit diagram of resistors in series is shown below. In the following circuit, two resistors are connected in series with the battery voltage ‘V’. In this type of connection, two resistors are normally connected one after another in a sequential way. So the flow of current throughout every resistor is identical.

The following circuit shows the equal resistance of the two resistors. In a series arrangement of resistors, the equal resistance can be given through the algebraic sum of each and every resistance.

Here, the equation for resistors in series can be derived.

The voltages across all two resistances are V1 and V2 where the flow of current throughout them is identical.

V = V1 + V2

Once the above equation is expanded then

IR = IR1 + IR2 => IR = I(R1+R2)

So, the resistors in series formula is

R = R1 + R2

#### Resistors in Series Voltage Drop

When the voltage is applied to a series circuit, then it is equivalent to the addition of the independent voltage drops. In a series circuit of resistors, the voltage drop across a resistor is equivalent to the resistor’s size.

If we want to calculate the voltage drop across individual resistors in a series circuit, then;

• Total resistance needs to calculate by adding each resistor value.
• Calculate the flow of current within the series circuit, which is similar across every resistor due to a single wire within the circuit.
• By using ohms law, calculate the voltage drop across every resistor.

### Resistors in Series Example Problems

Example1: The example problem to calculate the voltage drop in the series connection of resistors.
The circuit is designed with a 12V power source & two resistors R1 = 2 Ω & R2 = 4 Ω in series, then what is the voltage drop across every resistor?

First, the resistance can be calculated by adding all the resistances like 2 + 4 = 6 Ω.

After that, need to measure the flow of current in a circuit like 12 V/6 Ω = 2 A.

Now calculate the voltage drop across every resistor by using the current value with the help of ohms law (V = IR)

For 2 Ω resistor, the voltage drop V is = 2×2 = 4V

For 4 Ω resistor, the voltage drop V is = 2×4 = 8V

Example2: For the following series connection circuit, calculate the following quantities shown below…

• Equivalent Resistance
• Flow of Current
• The voltage drop across every resistor
• The power dissipation in every resistor

We know the values of R1 = 10 Ω, R2 = 20 Ω & R3 = 30 Ω, Voltage (V) = 100V. Three Resistors in Series Connection Problem

Equivalent Resistance

To calculate the equivalent resistance, add all resistor values like the following.

RT = R1 +R2 + R3

RT = 10 Ω + 20 Ω + 30 Ω

RT = 60 Ω

Flow of Current

The flow of current in the circuit can be calculated by the total resistance and voltage values.

I = V/RT

I = 100 V/60 Ω = 1.66A

The flow of current through resistors is same in series connection, So

Itotal = I1+I2+I3 = 1.66A

Voltage Drop across Every Resistor

The voltage drop at every resistor can be measured by using Ohm’s law.

We know that V = IR

So we know the values of I total = 1.66A

The voltage drop at R1 resistor is;

V1 = I*R1 = 1.66×10 = 16.6V

V2 = I*R2 = 1.66×20 = 33.2V

V3 = I*R3 = 1;.66×30 = 49.8V

VT= V1+ V2 + V3

100 V = 16.6 V + 33.2V + 49.8V

100 V = 99.6 V

Power Dissipation in Every Resistor

In the above circuit, three resistors are used so the power can be calculated for three resistors is

P1 = V1* Itotal => 16.6 x1.66 = 27.556

P2 = V2* Itotal => 33.2 x1.66 = 55.112

P3= V3* Itotal => 49.8 x1.66 = 82.668

In a series circuit, the highest resistance element consumes more power.

What does a resistor do?

A resistor in a circuit is used to restrict the current flow, signal levels can be adjusted, to divide voltages, active elements bias, etc.

Do resistors reduce current or voltage?

A resistor has the capacity to reduce current & voltage once connected to a circuit. According to Ohm’s law, once resistors in a circuit are increased, the current will be decreased.  Once current flows through resistors in a circuit, there will be a voltage drop across each resistor. So voltage changes directly with current (I).

What is the relationship between capacitor and resistor?

A Capacitor is used to store electric charge whereas a resistor is used to restrict the current flow in a circuit.

What happens if resistor and capacitor are connected in series?

If a resistor and a capacitor are connected in series to form an RC circuit, then the capacitor will charge up slowly throughout the resistor until the voltage across it reaches the voltage supply.

The advantages of resistors in series include the following.

• These circuits are simple to design.
• It works like a current regulator.
• The flow of current will stop if any component in the series connection breaks.
• The cost is low as compared to parallel.

The disadvantages of resistors in series include the following.

• In a series resistive circuit, if a single bulb is blown then there is no current flow within the circuit.
• If the loads like bulbs are increased, then the bulbs get dimmer.
• The series circuit resistance increases once more load is connected in the circuit.

### Applications

The applications of resistors in series include the following.

• Series resistive circuits are mainly used in low power-based circuits.
• These are used in voltage divider circuits.
• The series circuit connections are frequently used in electrical equipment.

Thus, this is all about an overview of resistors in series, working with example problems. The main characteristics of a series circuit are resistance, current, voltage, and voltage drop. Here is a question for you, what is are resistors in parallel?