How to solve a series circuit

Introduction: How to Solve a Basic Parallel or Series Circuit

How to solve a series circuit

By cxlmott Follow

How to solve a series circuit

How to solve a series circuit

When it comes to electrical engineering, solving circuits is a fundamental skill. Before beginning this instructable it is important to note the three main aspects of a circuit being current, voltage, and total resistance. Current (I) is how much physical electricity is running through each wire, which is measured in Amps. Potential difference, aka voltage (V) is measured in Volts, which is essentially the potential a circuit has to push electricity through the wire(s). Total resistance (R), measured in Ohms, is how much the circuit is resisting the flow of electricity. An entire circuit is shown in Fig. 1. Through this instructable you will learn how to solve for the total resistance of a circuit and then by using Ohm’s Law (I=V/R) to solve for the current (I) that a circuit will use.

Assumptions:

This instructable requires the basic knowledge of algebra along with the ability to use a calculator to solve algebraic equations. At Table 1 you can find tips for calculating the math values required in this instructable.

Step 1: Identify the Voltage (V) of the Circuit and Recognize the Type of Resistance

The voltage of a circuit is displayed by the symbol found in Fig. 1. You can simply transcribe this value and keep it until we are solving for current (I) in Step 3.

A Resistor is a small component of a circuit used to change how much resistance is within the circuit. It is illustrated as such in Fig. 2.These resistors can be organized in two basic ways, either in parallel or in series.

Parallel:

Parallel resistors look like a “ladder” on a circuit, each one is stacked on top of each other so to speak. This is illustrated in Fig. 3.

Series:

Series resistors look like a “string” on a circuit, each one is placed end-to-end in a row, all traveling in the same direction. This can be seen in Fig. 4. Look at the circuit you are given and identify which type of resistance your circuit uses, then you may proceed to step 2.

Step 2: Finding the Total Resistance

Because Ohm’s Law is found to be “I=V/R”, then we need one single, total value for resistance (R).

Series:

To find the total resistance of a series configuration, you simply add them together. For example, if you have three resistors R1, R2, and R3, the total resistance is as such “R=R1+R2+R3”. This is illustrated in Fig. 5.

Parallel:

To find the total resistance of a parallel configuration, we must divide one by each resistor value separately, add them together, then divide one by this total. Such as (1/R1 + 1/R2 + 1/R3) = 1/R ==> R=___. This is illustrated by Fig. 6. If you would like assistance with how to type these values into a calculator, please see Table 1.

Step 3: Solve for Current (I)

Once you have found the total resistance (R) and given voltage (V) we plug it into the Ohm’s Law equation (I=V/R). For example if our voltage was 4 Volts and our total resistance was 9 Ohm’s, then our current (I) would be 4/9 Amps, which is equal to 0.4444 Amps. Please see Fig. 7 for an illustration of this method.

Step 4: Try It for Yourself

As seen in Figures 8-11 there are four circuit examples.

Feel free to try each example while going through this instructable. The correct values for each example are found in Table 2 below.

Series Circuit and Voltage Division

Example 1: Find the total equivalent resistance in the following circuit

Solution

Example 2: For the following circuit:

  1. Find the total resistance
  2. Find the current i
  3. Find the voltage accross the 10Ω resistor

Solution

  1. Total resistance

The current can be calculated as

The voltage across the 10Ω resistor

Example 3: For the following circuit:

  1. Find the total resister value RT
  2. Find the current i
  3. Find the voltage across the individual resistors
  4. Verify Kirchhoff’s voltage law

Solution

    Total resistor value

The current can be calculated a

The voltage over the resistors

Example 4: For the following circuit:

  1. Find V1
  2. Find V2
  3. Verify Kirchhoff Voltage Law around a closed loop

Solution

Voltage Division:

In the following circuit, the current through all the resistor in series is
The equivalent resistor Req is sum of the resistor value.

To find the voltage drop vi across the resistor Ri, we use current and resistor value

A series circuit is a circuit that has only one path for current to flow. Because there is only one path for current flow, the current (A) is the same at any point in the circuit.

How to solve a series circuit

Ohm’s Law

The Ohm’s law formulas are used when finding unknown values in the circuit

How to solve a series circuit

V – Volts                   I – Current              R – Resistance

Voltage Drops in a Series Circuit

Voltage is the force that pushes the electrons through a resistance. The amount of voltage required is determined by the amount of current flow and resistance.  The amount of voltage necessary to push the current through each resistor is known as voltage drop. 

How to solve a series circuit

Voltage drop and be determined by placing a voltmeter across a resistor.   In a series circuit, the sum of all the voltage drops across all the resistors must equal the voltage applied to the circuit.

Resistance in a Series Circuit

Because only one path exists for the current to flow through a series circuit, it must flow through each resistor in the circuit. Each resistor limits or impedes the flow of current in the circuit. Therefore, the total amount of resistance to current flow in a series circuit is equal to the sum of the resistances in that circuit.

Rtotal = R1 + R2 + R3

Calculating Series Circuit Values

Three rules can be used with Ohm’s law for finding values of voltage, current, resistance, and power in any series circuit:

1. The current is the same at any point in the circuit.

2. The total resistance is the sum of the individual resistors.

3. The applied voltage is equal to the sum of the voltage drops across all the resistors.

How to solve a series circuit

The amount of current flow in the circuit can be found by using Ohm’s law:

How to solve a series circuit

If current is known then you can determine how many volts are required to push a certain amount of amps through the resistor

Solving Circuits

The first step in finding the missing values in the circuit is to find the total resistance (RT). This can be done using the second rule of series circuits, which states that resistances add to equal the total resistance of the circuit.

Rtotal = R1 + R2 + R3

The total resistance is then used to find the Current of the circuit.

How to solve a series circuit

Divide the total voltage of the circuit by the total resistance. Since the current is the same at any point in a series circuit, the voltage drop can also be determined for each resistor.

Power

Each resistors dissipates a certain amount of heat.(power) The power can be found using these formulas depending on the values known:

How to solve a series circuit

A good rule to remember when calculating values of electric circuits is that the total power used in a circuit is equal to the sum of the power used by all parts.

By the end of this section, you will be able to:

  • Draw a circuit with resistors in parallel and in series.
  • Calculate the voltage drop of a current across a resistor using Ohm’s law.
  • Contrast the way total resistance is calculated for resistors in series and in parallel.
  • Explain why total resistance of a parallel circuit is less than the smallest resistance of any of the resistors in that circuit.
  • Calculate total resistance of a circuit that contains a mixture of resistors connected in series and in parallel.

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 illustrated in Figure 1. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

Figure 1. (a) A series connection of resistors. (b) A parallel connection of resistors.

Resistors in Series

When are resistors in series? Resistors are in series whenever the flow of charge, called the current, must flow through devices sequentially. For example, if current flows through a person holding a screwdriver and into the Earth, then R1 in Figure 1(a) could be the resistance of the screwdriver’s shaft, R2 the resistance of its handle, R3 the person’s body resistance, and R4 the resistance of her shoes. Figure 2 shows resistors in series connected to a voltage source. It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence. (This fact would be an advantage to a person wishing to avoid an electrical shock, who could reduce the current by wearing high-resistance rubber-soled shoes. It could be a disadvantage if one of the resistances were a faulty high-resistance cord to an appliance that would reduce the operating current.)

Figure 2. Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).

To verify that resistances in series do indeed add, let us consider the loss of electrical power, called a voltage drop, in each resistor in Figure 2. According to Ohm’s law, the voltage drop, V, across a resistor when a current flows through it is calculated using the equation V = IR, where I equals the current in amps (A) and R is the resistance in ohms (Ω). Another way to think of this is that V is the voltage necessary to make a current I flow through a resistance R. So the voltage drop across R1 is V1 = IR1, that across R2 is V2 = IR2, and that across R3 is V3 = IR3. The sum of these voltages equals the voltage output of the source; that is,

This equation is based on the conservation of energy and conservation of charge. Electrical potential energy can be described by the equation PE = qV, where q is the electric charge and V is the voltage. Thus the energy supplied by the source is qV, while that dissipated by the resistors is

Making Connections: Conservation Laws

These energies must be equal, because there is no other source and no other destination for energy in the circuit. Thus, qV = qV1 + qV2 + qV3. The charge q cancels, yielding V = V1 + V2 + V3, as stated. (Note that the same amount of charge passes through the battery and each resistor in a given amount of time, since there is no capacitance to store charge, there is no place for charge to leak, and charge is conserved.) Now substituting the values for the individual voltages gives

Note that for the equivalent single series resistance Rs, we have

This implies that the total or equivalent series resistance Rs of three resistors is Rs = R1 + R2 + R3. This logic is valid in general for any number of resistors in series; thus, the total resistance Rs of a series connection is

as proposed. Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up.

Example 1. Calculating Resistance, Current, Voltage Drop, and Power Dissipation: Analysis of a Series Circuit

Suppose the voltage output of the battery in Figure 2 is 12.0 V, and the resistances are R1 = 1.00 Ω, R2 = 6.00 Ω, and R3 = 13.0 Ω. (a) What is the total resistance? (b) Find the current. (c) Calculate the voltage drop in each resistor, and show these add to equal the voltage output of the source. (d) Calculate the power dissipated by each resistor. (e) Find the power output of the source, and show that it equals the total power dissipated by the resistors.

Strategy and Solution for (a)

The total resistance is simply the sum of the individual resistances, as given by this equation:

Strategy and Solution for (b)

The current is found using Ohm’s law, V = IR. Entering the value of the applied voltage and the total resistance yields the current for the circuit:

Strategy and Solution for (c)

The voltage—or IR drop—in a resistor is given by Ohm’s law. Entering the current and the value of the first resistance yields

How to solve a series circuit

Series circuits connect resistors such that the current, measured by amplitude or amperage, follows one path in the circuit and remains constant throughout. The current flows in the opposite direction of electrons through each resistor, which impede the flow of electrons, one after another in a single direction from the positive end of the battery to the negative. There are no external branches or paths through which the current can travel, as there would be in a parallel circuit.

Series Circuit Examples

Series circuits are common in everyday life. Examples include some types of Christmas or holiday lights. Another common example is a light switch. Additionally, computers, televisions and other household electronic devices all work through the concept of a series circuit.

In a series circuit, amperage, or amplitude, of the current remains constant and can be calculated using Ohm’s law ​V = I/R​ while the voltage drops across each resistor that can be summed up to get the total resistance. In contrast, in a parallel circuit, the amplitude of a current changes across the branching resistors while voltage remains constant.

Amperage (or Amps) in a Series Circuit

You can calculate the amplitude, in amps or amperes given by the variable A, of the series circuit by summing up the resistance at each resistor in the circuit as ​R​ and summing up the voltage drops as ​V​, then solving for I in the equation ​V = I/R​ in which ​V​ is the voltage of the battery in volts, ​I​ is current, and ​R​ is the total resistance of the resistors in ohms (Ω). The voltage drop should be equal to the voltage of the battery in a series circuit.

The equation ​V = I/R​, known as Ohm’s Law, also holds true at each resistor in the circuit. The current flow throughout a series circuit is constant, which means it’s the same at each resistor. You can calculate the voltage drop at each resistor using Ohms’ Law. In series, the voltage of the batteries are increased, meaning they last a shorter length of time than if they were in parallel.

Series Circuit Diagram and Formula

How to solve a series circuit

In the above circuit, each resistor (denoted by zig-zag lines) is connected to the voltage source, the battery (denoted by the + and – surrounding the disconnected lines), in series. Current flows in one direction and remains constant at each part of the circuit.

If you summed up each resistor, you would get a total resistance of 18 Ω (ohms, where ohm is the measure of resistance). This means you can calculate current using ​V = I/R​ in which ​R​ is 18 Ω and ​V​ is 9 V to get a current I of 162 A (amps).

Capacitors and Inductors

In a series circuit, you can connect a capacitor with a capacitance ​C​ and let it charge over time. In this situation, current across the circuit is measured as

The total capacitance of a series circuit is given by

in which each the inverse of each individual capacitor is summed on the right side (​1/C​​1​, ​1/C​​2​, etc.). In other words, the inverse of the total capacitance is the sum of the individual inverses of each capacitor. As time increases, the charge on the capacitor builds and the current slows down and approaches, but never fully reaches, zero.

Similarly, you can use an inductor to measure current

in which the total inductance L is the sum of the inductance values of the individual inductors, measured in Henries. When a series circuit builds charge as a current flows, the inductor, a coil of wire that usually surrounds a magnetic core, generates a magnetic field in response to the flow of current. They can be used in filters and oscillators,

Series vs. Parallel Circuits

When dealing with circuits in parallel, in which the current branches through different parts of the circuits, the calculations are “flipped.” Instead of determining the total resistance as the sum of individual resistances, the total resistance is given by

(the same way of calculating total capacitance of a series circuit).

The voltage, not the current, is constant throughout the circuit. The total parallel circuit current equals the sum of the current across each branch. You can calculate both current and voltage using Ohm’s Law (​V = I/R​).

How to solve a series circuit

In the parallel circuit above, the total resistance would be given by the following four steps:

  1. 1/Rtotal​ = 1/R1 + 1/R2 + 1/R3
  2. 1/Rtotal​ = 1/1 Ω + 1/4 Ω + 1/5 Ω
  3. 1/Rtotal​ = 20/20 Ω + 5/20 Ω + 4/20 Ω
  4. 1/Rtotal​ = 29/20 Ω
  5. Rtotal = 20/29 Ω or about .69 Ω

In the above calculation, note that you can only reach step 5 from step 4 when there is only one term on the left side (​1/Rtotal ​) and only one term on the right side (29/20 Ω).

Likewise, the total capacitance in a parallel circuit is simply the sum of each individual capacitor, and the total inductance is also given by an inverse relationship (​1/L​​total​ ​= 1/L​​1​ ​+ 1/L​​2​ ​+ …​ ).

Direct Current vs. Alternating Current

In circuits, current can either flow constantly, as is the case in a direct current (DC), or fluctuate in a wave-like pattern, in alternating current circuits (AC). In an AC circuit, current changes between a positive and negative direction in the circuit.

British physicist Michael Faraday demonstrated the power of DC currents with the dynamo electric generator in 1832, but he couldn’t transmit its power over long distances and the DC voltages required complicated circuits.

When the Serbian-American physicist Nikola Tesla created an induction motor using AC current in 1887, he demonstrated how it easily transmitted over long distances and could be converted between high and low values using transformers, a device used to change voltage. Soon enough, around the turn of the 20th-century households across America began discontinuing DC current in favor of AC.

Nowadays electronic devices use both AC and DC when appropriate. DC currents are used with semiconductors for smaller devices that only need to be turned on and off such as laptops and cell phones. AC voltage is transported through long wires before it is converted to DC using a rectifier or diode to power these appliances like light bulbs and batteries.

In this interactive object, learners solve for total resistance and current, the current through each resistor, the voltage across each resistor, and the power dissipated.

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How to solve a series circuit

A series circuit, also known as a simple circuit, is a circuit in which there is only one path for current to follow. It can have resistors, inductors, capacitors, light bulbs, and other things connected, but as long as there is a single path from positive to negative in the circuit, the circuit is in series. See the figure below.

According to Kirchoff’s Voltage Law, the sum of all voltages in a series circuit will add up to the source voltage (VS) (or, as some understand it, the sum of all voltages subtracted from the source voltage will be equal to zero). The reason behind this is because whatever voltage is fed into a series circuit (sometimes called the Voltage Rise) has to go somewhere. Every component in a circuit that has current flowing through it and a resistive value will have what’s known as a Voltage Drop. The relationship behind this law is referred to as Ohm’s Law, which is signified by the triangle below.

The triangle means the following:

Voltage (V) / Current (I) = Resistance (R)

Voltage (V) / Resistance (R) = Current (I)

Resistance (R) * Current (I) = Voltage (V)

*Note: Voltage (V) can also be signified by an E.

If the sum of all voltages has to add up to the equivalent value of the source voltage, then that would mean that one of the values in Ohm’s Law would have to be a constant. In the case of the series circuit, the constant value would be that of the current. Whatever the value of the current is when it enters the circuit is the same value of the current at the ‘end’ of the circuit. Confused? See the diagram below.

With Ohm’s Law we can identify the theoretical value of each component in a series circuit. For example, if I have a 10 V battery connected to a series circuit with a resistor with a value of 100 ohms (ohms being the units for resistance), and we then proceed to connect another resistor of an unknown value to the circuit, we can calculate the value of the second resistor. We can also prove that the current going through the second resistor is equal to the current going through the first resistor. Don’t believe me? Take a look.

First we need to find the voltage at R2. Since, according to Kirchoff’s Voltage Law, the voltages at the resistors would have to add up to the source voltage (V1 + V2 = VS), we can deduce that V2 = VS – V1. Of course, that would mean that we would need to know V1. No problem!

V1 = I * R1 (Ohm’s Law)

V1 = 2 milliAmps (mA) * 1000 Ohms

If we know that V1 = 2 Volts, then that means that:

V2 = 10 V – 2 V = 8 Volts.

Everything is starting to come together now. We know that V2 is equal to 8 Volts, and since we have two known values at R2 (the voltage and the current), we can now find the value of the resistor.

R2 = V/I (Ohm’s Law)

*Note: The values used in this circuit are unrealistic. They were only chosen to show a simple example.

Now that we know the values for both resistors and the voltages at each, we can prove that the current running through the circuit is the same value at every point.

I (Current) = V/R (Ohm’s Law)

I = 8 V / 4000 Ohms

I = 0.002 Amps (2 mA)

It’s a match to our original current!

Series circuits are used in a variety of simple electronics, such as in the book lights that you buy at the dollar store (open one up and take a look!). There are many applications for simple circuits, some of which would surprise you. For further reading on simple circuits and how they apply to electronics, see any textbook about the fundamentals of electronics. Various websites also provide easy explanations and experiments that anyone can understand and do. If you would like to read about some interesting electrical facts, see: How to Do Calculations for a Parallel Circuit.

In a series circuit components like resistors and loads are connected in a single path. Current must go through every component in order starting from the positive terminal of the battery through everything in order and back to the negative battery terminal.

Series Circuit Handout to go along with the problems on this page and the PhET lab at the end.

  • Practice and Series Circuit Virtual Lab Sheet

How to solve a series circuit

Series Circuits vs. Parallel Circuits

Series Circuits only have one path while parallel circuits we will see in a later unit have branches. Compare the pictures below each with three resistors.

How to solve a series circuit

Lights in a Series Circuit Compared to a Parallel Circuit

When lights are connected in a series circuit and one goes out the circuit becomes open and no other light works. This is because there is no path to the negative terminal of the battery when a circuit is open.

When lights are connected in parallel circuit and one light goes out the remaining ones stay on. No current will flow down the branch with the disconnected light bulb since that branch is open. Current will follow the other paths to the negative terminal of the battery leaving the other lights on.

Series Circuit Diagrams

To keep the models simple we will only places a battery and resistors in the circuits of our diagrams on this page. Remember that the longer line in the battery symbol is the positive terminal and the shorter line is the negative terminal. The convention is to have current run from the positive terminal to the negative terminal. Due to this convention the resistors are numbered in order. Here the resistors get their number resistor 1, resistor 2, and resistor 3 based on the flow of current starting from the positive terminal of the battery.

Series Circuit Rules

Voltage Drop In A Series Circuit

In a series circuit voltage drops across each resistor until the entire amount provided by the battery has dropped. If you add all the individual voltage drops of a series circuit together you can determine the voltage of the entire circuit (VT) found at the power source.

Current in a Series Circuit

There is only one path in a series circuit for current to travel on. All current must run from the positive terminal to the negative terminal of the power source. Observe the animation of how the same current has to flow through every component of the circuit in series.

Resistance in a Series Circuit

Any resistor or load (device with a resistance) in a series acts like a speed bump in a series slowing current down. Since there is only one conductive path in series every device adds to total resistance.

Note that a wire itself has resistance and the less conductive a wire is the more resistance it would add to a circuit. We will ignore this in our examples below for simplicity and pretend the wire was 100% conductive.

How to solve a series circuit

How to solve a series circuit

Circuit Equations

Ohm’s Law (V=IR), Voltage equals current times resistance, can be used anywhere in the circuit but only at a single location.

See all the squares in red above, if you are using Ohm’s law you can only use information in that location, the V,I, and R within a single square.

The location can be an individual resistor, for example resistor one with the variables Voltage (V1), Current (I1), Resistance (R1). The location can also be at the battery, which is a measure that represents the overall circuits voltage (VT), current (IT), and Resistance (RT).

At the battery the subscript T (ex. VT) stands for total or of the circuit. Some equations sheets may use emf (ex. Vemf) or another notation, if there is any subscript other than a number it will likely be of the circuit.

When you are using information between different red blocks you must use the series circuit rules.

Start any problem by drawing out the circuit and have every resistor labeled as you see in the picture above. Then write in all your givens. Next, follow the basic steps to a series circuit problem.

Basic Steps To A Series Circuit Problem

#1 See if you can do Ohm’s Law (V=IR) at any location in the circuit.

#2 See if you have current anywhere because that current will be the same everywhere following the series circuit rule below.

#3 Check if you can do any of the other series circuit rules.

You will continue to follow these steps over and over until everything in the circuit is complete. Follow our examples below until you feel comfortable to follow the steps solving series circuit problems on your own.

The series circuit rules show how to apply Ohm’s law when the circuit has more than one device receiving electrical energy.

It will also help us see how the current, the resistance, and the voltage change in the circuit. Below is an example of a series circuit. The circuit has 1 switch (green), 1 voltage source of 12 volts, and 3 resistors. 

A circuit is in series if the current has a single pathway.

Simply put, the current cannot “make choices” as to where it would go. If the current can either go this way or that way, then the circuit is not in series.

How to solve a series circuit

Look carefully at the circuit above and you will see that the current has to go through the path it is in. This fact leads us to Rule #1.

Rule #1: In series circuits, the current passing through each electrical device is the same.

Let I be the current going through the circuit

Let I1 be the current going through the 1 Ohm resistor.

Let I2 be the current going through the device with 2 Ohms resistor.

Let I3 be the current going through the 3 Ohms resistor.

This series circuit has 3 resistors. Recall that a resistor is a device that resists the flow of current. Does it make sense to you that the current will be resisted by all 3 resistors? It will indeed!

Rule #2: In series circuits, the total resistance is found by adding the individual resistance of all resistors in the circuit.

For example, to find the total resistance for our circuit above, just add 1, 2, and 3.

Total resistance = 1 + 2 + 3 = 6 Ohms.

We can now use Ohm’s law to find the intensity of the current flowing through the circuit.

Whenever the current go through a device, a voltage drop or potential difference occurs because of the resistor in that device. It simply means that the voltage in that device will not be the same as the voltage source. 

Voltageacross 1 Ohm resistor = R × I = 1 × 2 = 2 volts

Voltageacross device with 2 Ohms resistor = R × I = 2 × 2 = 4 volts

Voltageacross 3 Ohms resistor = R × I = 3 × 2 = 6 volts

From this, there is an important observation we need to make.

Notice that 12 volts  = 2 + 4 + 6

Rule #3: In series circuit, the voltage supplied by the source is the sum of the individual voltage drop at each device.

Let V be the voltage at the source

Let v1 be the voltage across the 1 Ohm resistor.

Let v2 be the voltage across the device with 2 Ohms resistor.

Let v3 be the voltage across the 3 Ohms resistor.

Series circuit rules generalization

The series circuit rules can be summarized and generalized as follow:

Let I be the current going through the circuit

Let I1, I2. In be the current going through other devices.

Let R1, R2. Rn be the resistance of devices in the circuit.

Let V be the voltage at the source

Let v1,v2. vn be the voltage drop across other devices.

Series circuit quiz

Take the series circuit quiz below to see how well you understand series circuit. After completing this quiz with 100% accuracy, you will know exactly how the current, the voltage, and the resistors behave in a series circuit. You will not need to use a paper and pencil to complete this quiz.

An electrical circuit is a combination of two or more components that are connected together to obtain some output. Very often the components are connected in series to form a series circuit. In this post, you’ll learn everything important about the series circuits. Let’s start it.

What is a series circuit and how to identify it

A series circuit is the one in which one end of two components are connected together and there is no other connection between them. Consider the circuit below:

How to solve a series circuitFigure 1: A series circuit

Resistor R1 connects to resistor R2 and there is no other component between them, both of these resistors are in series. Similarly, the resistor R2 and negative terminal of voltage source are connected to each other and there is no other connection between them. Resistor R2 and source V are also in series. Finally, the positive terminal of V and one end of resistor R are also in series. Since all components are in series, the overall circuit is referred to a series circuit.

How resistance behaves in series

The overall resistance of circuit is sum of individual resistors.

Let’s again consider the Figure 1.

The overall resistance Req is sum of two resistors in series.

Mathematically, Req = R1 + R2

Example: Let’s assume R1 = 10 ohms and R2 = 7 ohms then Req = 5 ohms

The figure below illustrates this:

How to solve a series circuitFigure 2: How to solve resistors in series

How current behaves in series

The electric current through a series circuit adjusts itself in such manner that the same current flows through all components. In actual the current is the ratio of voltage to the overall resistance of the circuit. The electrical current always remains same through series components. If 5 A current flows through resistance R2 then same 5 A will flow through 7 A current.

Suppose in the first circuit of figure 2. The value of the voltage source is 24 volts. Then current I = V/R = 24 V / 12 ohms = 2 Amps flows through the entire circuit.

How voltage behaves in series

The electrical voltage in series circuit divides between components. The higher the value of resistance is, the more voltage is dropped across it. Let’s again consider the case discussed in the previous section. From current of 2 Amps, the voltage V = IR across resistors are calculated by Ohms law: