Resisitors in Series
The total resistance in the circuit with resistors connected in series is equal to the sum of the individual resistances.
Learning Objective

Calculate the total resistance in the circuit with resistors connected in series
Key Points
Terms

series
A number of things that follow on one after the other or are connected one after the other.

resistance
The opposition to the passage of an electric current through that element.
Full Text
Overview
Most circuits have more than one component, called a resistor, that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance. The simplest combinations of resistors are the series and parallel connections. The total resistance of a combination of resistors depends on both their individual values and how they are connected.
Resistors in Series
Resistors are in series whenever the flow of charge, or the current, must flow through components sequentially .
Resistors in Series
These four resistors are connected in series because if a current was applied at one end, it would flow through each resistor sequentially to the end.
shows resistors in series connected to a voltage source. The total resistance in the circuit is equal to the sum of the individual resistances, since the current has to pass through each resistor in sequence through the circuit.
Resistors connected in a series circuit
Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).
Using Ohm's Law to Calculate Voltage Changes in Resistors in Series
According to Ohm's law, the voltage drop, V, across a resistor when a current flows through it is calculated by using the equation V=IR, where I is current in amps (A) and R is the resistance in ohms (Ω).
So the voltage drop across R_{1} is V_{1}=IR_{1}, across R_{2} is V_{2}=IR_{2}, and across R_{3} is V_{3}=IR_{3}. The sum of the voltages would equal: V=V_{1}+V_{2}+V_{3}, based on the conservation of energy and charge. If we substitute the values for individual voltages, we get:
or
This implies that the total resistance in a series is equal to the sum of the individual resistances. Therefore, for every circuit with N number of resistors connected in series:
Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up.
Since voltage and resistance have an inverse relationship, individual resistors in series do not get the total source voltage, but divide it. This is indicated in an example of when two light bulbs are connected together in a series circuit with a battery. In a simple circuit consisting of one 1.5V battery and one light bulb, the light bulb would have a voltage drop of 1.5V across it. If two lightbulbs were connected in series with the same battery, however, they would each have 1.5V/2, or 0.75V drop across them. This would be evident in the brightness of the lights: each of the two light bulbs connected in series would be half as dim as the single light bulb. Therefore, resistors connected in series use up the same amount of energy as a single resistor, but that energy is divided up between the resistors depending on their resistances.
Key Term Reference
 Component
 Appears in these related concepts: Adding and Subtracting Vectors Using Components, Cathode Ray Tube, TV and Computer Monitors, and the Oscilloscope, and Position, Velocity, and Acceleration as a Function of Time
 Law
 Appears in these related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 Ohm's law
 Appears in these related concepts: Energy Usage, Root Mean Square Values, and Resistors in AC Circuits
 battery
 Appears in these related concepts: Fuel Cells, The Battery, and Sources of EMF
 circuit
 Appears in these related concepts: Combinations of Capacitors: Series and Parallel, Microwaves, and Maxwell's Equations
 conservation
 Appears in these related concepts: Conservation of Mechanical Energy, Museums and Private Collections, and Linear Momentum
 current
 Appears in these related concepts: Reporting LongTerm Liabilities, Magnetic Force Between Two Parallel Conductors, and The Junction Rule
 energy
 Appears in these related concepts: Surface Tension, Energy Transportation, and Introduction to Work and Energy
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 inverse
 Appears in these related concepts: Inverse Functions, The Law of Universal Gravitation, and Hyperbolic Functions
 ohm
 Appears in these related concepts: Resonance in RLC Circuits, Poiseuille's Equation and Viscosity, and Phase Angle and Power Factor
 parallel
 Appears in these related concepts: Resistors in Parallel, Combination Circuits, and How Skeletal Muscles Are Named
 resistor
 Appears in these related concepts: Impedance, The Loop Rule, and Introduction and Importance
 simple circuit
 Appears in these related concepts: Current and Voltage Measurements in Circuits, Ohm's Law, and Overview of Electric Current
 voltage
 Appears in these related concepts: The Nernst Equation, Electric Potential Due to a Point Charge, and Principles of Electricity
Sources
Boundless vets and curates highquality, openly licensed content from around the Internet. This particular resource used the following sources: