## Resistors in Series

### Designing with resistors in series

Let's see what happen when the resistors are connected in series. How to calculate total resistance if n number of resistors are connected in series as shown in figure. The Total resistance Req will be:

$$\mathsf{ R_{eq} = R_1 + R_2 + R_3 + \; ... \; + R_{n} \\ (or) \\ R_{eq} = \sum_{i=1}^n R_i }$$

#### Voltage

The total voltage that appears across a series resistors network is the addition of voltage drops at each individual resistances. In the above figure we have three different resistors which have three different values of voltage drops at each stage.

Total voltage that appears across the circuit:

$$\mathsf{V\:\:=\:\:V_{1}\:+\:V_{2}\:+\:V_{3}\:+\;...\;\:+\:V_{n}}$$

Where V1 is the voltage drop of 1st resistor, V2 is the voltage drop of 2nd resistor and Vn is the voltage drop of nth resistor in the above circuit.

#### Current

The total amount of Current that flows through a set of resistors connected in series is the same at all the points throughout the resistor network. Hence, the current is the same when measured at the input or at any point between the resistors or even at the output.

Current through the circuit:

$$\mathsf{I\:\:=\:\:I_{1}\:=\:I_{2}\:=\:I_{3}\:=\;...\;\:=\:I_{n} }$$

Where I1 is the current through the 1st resistor, I2 is the current through the 2nd resistor and In is the current through the nth resistor in the above circuit.

#### Example circuit

Let's take an example circuit, 3 resistors have resistance value 2 ohm, 4 ohm, and 8 ohm respectively are connected as series. This circuit shown in below. 1. Find the voltage drop of each resistor and the current through this circuit, If Vin equal to 5V.

First, we need to find total resistance, As we know in a series circuit, the total resistance is equal to the sum of each resistance value. i.e,

$$\mathsf{ R = 2\Omega +4\Omega +8\Omega \\ R = 14\Omega. }$$

From Ohm's Law, $\mathsf{ I = \frac{V}{R}}$.

So the current,

$$\mathsf{ I = \frac{5}{14} \;= \; 0.357 A \; \text{or} \; 357mA. }$$

The Voltage drop on 2Ω resistor is:

Again from Ohm's Law $\mathsf{ V = IR}$.

$$\mathsf{ V = 0.357 x 2 = 0.714V. }$$

Similarly,

The Voltage drop on 4Ω resistor is $\mathsf{ 0.357 x 4 = 1.428V}$.

The Voltage drop on 8Ω resistor is $\mathsf{ 0.357 x 8 = 2.856V}$.

NOTE: The total resistance value of the resistors which are in series would be greater than the maximum resistance value of the resistor is in that series circuit.