## Series Circuit

Series circuits are those circuits which provide only one path for current to flow between two points. In series circuits, current remains same but voltage is different across each resistor. The voltage variation depends on the value of resistor.

## Series Connection

Following figures are showing the different configuration of series circuits. For each case, circuits are connected in series arrangement and current is same for each. Figure 1(a) showing the series circuit connection by two resistors **R _{1}** and

**R**while Figure 1(b) showing the three resistances (

_{2}**R**,

_{1}**R**, and

_{2}**R**).

_{3}Figure 1:Series circuits representation

## Series Resistance Formula

Series resistance formula calculate the total resistance in a circuit. It is also known as total resistance of a circuit. The circuit calculation becomes very easy with the help of total resistance. Let suppose we want to find out the total resistance in a circuit of given figure 1(a), then we will calculate it as:

**R _{T} = R_{1} + R_{2}**

Similarly, for figure 1(b) the total resistance formula will be as

**R _{T} = R_{1} + R_{2} +R_{3}**

In general, we can say that total resistance of a series circuit is just an addition of individual resistances such as:

**R _{ T } = R_{ 1 } +R_{ 2 }+R_{ 3 }+,…,+ R_{ N }**

## Current in a Series Circuit

We already described that current in series circuit will always be same. The reason for same current is that current is not divided into whole circuit and uniformly flow from each resistor. Let suppose we want to find out the current in series circuit shown in figure 2. This circuit consists on three resistances and one voltage source. By using the Ohm’s law:

**-V _{ in } +IR_{ 1 }+ IR_{ 2 }+ IR_{ 3 } = 0**

Since the current is same for each case, therefore takingthe current common and we get:

**I (R _{ 1}+R_{ 2}+R_{ 3 }) = V_{ in}**

or

** I =V _{ in } / (R_{ 1 }+R_{ 2}+R_{ 3 })**

Figure 2:Current flowing through series resistance

## Voltage in a Series Circuit

Voltage in series circuit is always different. The reason for different voltage is that each resistance has different value and voltage drop is different for each case. Let’s find out the voltage drop across each resistor by considering the circuit shown in figure 3.

Figure 3:Voltage measurement for each resistor

Since we already determined the current for each case, the voltage across each resistor is just multiplication of current and resistor such as:

**V _{ R1 } = IR_{ 1 }**

**V _{ R2 } = IR _{ 2 }**

*V _{ R3 } = IR_{ 3 }*

While the total voltage will be the sum of each voltage and mathematically it will be represented as:

**V _{ in } = V_{ R1 } + V_{ R2 } + V_{ R3 }**

I’m also attaching the video how to obtain the value of current and voltage across each resistor and current in a loop.