# SERIES RESISTOR

### IDIOMA (LANGUAGE) : ESPAÑOL

It is said that a set of resistors connected in series has the same current flowing through them. In a series resistor grid, the amount of current that flows will be the same at all connection points.

IR1=IR2=IR3=IAB

Consider the following series resistive circuit

Here the resistors R1, R2 and R3 each with values 1Ω, 2Ω and 3Ω respectively are connected in series, that is why the same current will flow through all the resistors. The total resistance of the circuit is equal to the sum of the individual resistors.

Here the resistors R1, R2 and R3 each with values 1Ω, 2Ω and 3Ω respectively are connected in series, that is why the same current will flow through all the resistors. The total resistance of the circuit is equal to the sum of the individual resistors.
If RT is the total resistance, then
RT=R1+R2+R3

Now the equivalent resistance of the circuit is

REQ=R1+R2+R3

REQ=1+2+3

REQ= 6
The resistors in series combination can be replaced by a single resistor REQ of the value of 6Ω.

## VOLTAGE CALCULATION

For resistors connected in series, the voltage in each resistor does not follow the same rule as the current. In the case of series resistors, the total voltage across the resistors is equal to the sum of the individual potential differences in each resistor.

In the previous circuit, the potential difference in each resistor can be calculated using Ohm’s Law. In the series circuit flows a current of 1A, therefore, according to Ohm’s Law:

The potential difference through the resistance R1 is:
I × R1 = 1 × 1 = 1V
The potential difference through the resistance R2 is:
I × R2 = 1 × 2 = 2V
The potential difference through the resistance R3 is:
I × R1 = 1 × 3 = 3V

Therefore, the total voltage:

VAB = 1 V + 2 V + 3 V = 6 V
Consider a series connection of three resistors R1, R2 and R3 with the current I flowing through them. Let the potential fall from A to B. This fall of potential is the sum of the individual fall of potential across each individual resistor. Then, according to Ohm’s Law the fall of potential through R1 is
VR1 = I x R1
The fall of potential through R2 is
VR2 = I x R2
The fall of potential through R3 is
VR3 = I x R3
∴ V = VR1 + VR2 + VR3
∴V = I × R1 + I × R2 + I × R3
If the equivalent resistor of the resistors connected in series in the previous circuit is REQ, then
𝑉 = 𝐼 × 𝑅EQ
In the case there are n resistors in the series R1, R2…Rn, then the voltage across them is the sum of the individual potential difference in each resistor.
VT = VR1 + VR2 + ..... + VRn

In a combination of series resistors of n resistors, if the resistive value of each resistor is different from the other, then the potential at each resistor is different.

## APPLICATIONS

When two resistors of different resistance value are connected in series, the voltage across them is different, this method is the basis for voltage divider circuits.

If the resistor in a voltage divider circuit is replaced with a sensor, then the amount of voltage that is detected becomes an electrical signal that can be easily measured. The sensors used frequently are thermistors and light-dependent resistors. In the thermistor, the resistor varies according to the temperature, for example, suppose that the thermistor has a resistance of 20 kΩ at a temperature of 20°C, the same thermistor can have a resistor of 150 Ω at a temperature of 70°C, therefore, the fall of potential in the thermistor will be different depending on the temperature. This resistor change according to the temperature can be calibrated to find the temperature value from the fall of potential through the thermistor.

Another sensor that uses a resistor in series combination is the Photo resistor or Light dependent resistor, it is a light-dependent resistor, the resistance varies according to the intensity of the light incident on them. In the absence of light, the resistive value of a typical light-dependent resistor is as high as 1 MΩ, in the presence of light, the value of the light-dependent resistor falls to a small value generally of the order of few ohms. This variation in resistance in coordination with the intensity of the light will result in different voltage drops. The voltage drop can be calibrated to find the presence of the light of a certain wavelength.

electronicErick Méndezresistor