Basic Electronics On The Go - Resistors in Series

From http://www.electronicshub.org/resistors-in-series/

Introduction

Resistors are the basic components of any electrical or electronic circuit. Often resistors are found in large numbers irrespective of the size of the circuit. Resistors can be connected in series or in parallel or a combination of both. In order to reduce the complications of different combinations of resistors, some rules are to be followed.

Two resistors are said to be in series when same current flows through them. Resistors in series can be replaced by a single resistor. All the resistors follow the basic laws like Ohm’s law and Kirchhoff’s current law irrespective of their combination and complexity.

Resistors in Series

A set of resistors are said to be in series when they are connected back to back in a single line. The same current will flow through all the resistors. Resistors in series are said to have common current.

In a series resistor network, the amount of current that flows will be same at all points.

IR1 = IR2 = IR3 = IAB.

Consider the following series resistive circuit

Here the resistors R1, R2 and R3 each valued 1 Ω, 2 Ω and 3 Ω are in series connection. Same current will flow through all the resistors since they are connected in series. The total resistance of the circuit is equal to sum of individual resistances.

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 Ω + 2 Ω + 3 Ω

REQ = 6 Ω

The  Equivalent Resistance of the circuit  is used to replace any number resistors in series.

Voltage Calculation

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

In the above circuit, the potential difference across each resistor can be calculated using Ohm’s Law. The series circuit has a current of 1 A flowing. Then according to Ohm’s law

Potential difference across the resistor R1 is I × R1 = 1 × 1 = 1 V.

Potential difference across the resistor R2 is I × R2 = 1 × 2 = 2 V.

Potential difference across the resistor R3 is I × R3 = 1 × 3 = 3 V.

Therefore the total voltage VAB = 1V + 2V+ 3V = 6 V.

Consider a series connection of three resistors R­1, R2 and R3 with current I flowing through them.

Let the potential drop from A to B be V. This potential drop is sum of individual potential drops across each individual resistor. Then according to Ohm’s law

The potential drop across R­1 is VR1 = I × R­1

The potential drop across R2 is VR2 = I×R2

The potential drop across R3 is VR3 = I×R3

∴ V = VR1 + VR2 + VR3

∴V = I × R1 + I × R2 + I × R3

N resistors in series combination each with different resistance will have N different potential differences across them. This type of circuit will form a Voltage Divider. Voltage divider circuit is the basis of construction of Potentiometer.

In a series circuit, the values of voltage, current or resistance can be calculated using Ohm’s law. The resistors can be interchanged in a series circuit without affecting the total power to each resistor, current or total resistance of the circuit.

Applications

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

If one resistor in a voltage divider circuit is replaced with a sensor, then the quantity being sensed is converted to an electrical signal which is easily measured. The frequently used sensors are thermistors and light dependent resistors.In thermistor, the resistance varies according to temperature. For example, assume that thermistor has a resistance of 10 KΩ at a temperature of 250C. The same thermistor can have a resistance of 100 Ω at a temperature of 1000C. Hence the potential drop across the thermistor will be different based on the temperature. This change of resistance according to temperature can be calibrated to find the value of temperature from the potential drop across the thermistor.


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