# Connexions

You are here: Home » Content » College Physics » Ohm’s Law: Resistance and Simple Circuits
Content endorsed by: OpenStax College

• Preface

• #### 34. Frontiers of Physics

• 35. Atomic Masses
• 37. Useful Information
• 38. Glossary of Key Symbols and Notation

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Endorsed by (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
• OpenStax College

This collection is included in aLens by: OpenStax College

Click the "OpenStax College" link to see all content they endorse.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• Pierpont C & TC

This module is included inLens: Pierpont Community & Technical College's Lens
By: Pierpont Community & Technical CollegeAs a part of collection: "College Physics -- HLCA 1104"

Click the "Pierpont C & TC" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

• Featured Content

This collection is included inLens: Connexions Featured Content
By: Connexions

"This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. […]"

Click the "Featured Content" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Order printed collection

Inside Collection (Textbook):

Textbook by: OpenStax College. E-mail the author

# Ohm’s Law: Resistance and Simple Circuits

Module by: OpenStax College. E-mail the author

Summary:

• Explain the origin of Ohm’s law.
• Calculate voltages, currents, or resistances with Ohm’s law.
• Explain what an ohmic material is.
• Describe a simple circuit.

What drives current? We can think of various devices—such as batteries, generators, wall outlets, and so on—which are necessary to maintain a current. All such devices create a potential difference and are loosely referred to as voltage sources. When a voltage source is connected to a conductor, it applies a potential difference VV size 12{V} {} that creates an electric field. The electric field in turn exerts force on charges, causing current.

## Ohm’s Law

The current that flows through most substances is directly proportional to the voltage VV size 12{V} {} applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied:

IV.IV. size 12{I prop V.} {}
(1)

This important relationship is known as Ohm’s law. It can be viewed as a cause-and-effect relationship, with voltage the cause and current the effect. This is an empirical law like that for friction—an experimentally observed phenomenon. Such a linear relationship doesn’t always occur.

## Resistance and Simple Circuits

If voltage drives current, what impedes it? The electric property that impedes current (crudely similar to friction and air resistance) is called resistance RR size 12{R} {}. Collisions of moving charges with atoms and molecules in a substance transfer energy to the substance and limit current. Resistance is defined as inversely proportional to current, or

I1R.I1R. size 12{I prop { {1} over {R} } "."} {}
(2)

Thus, for example, current is cut in half if resistance doubles. Combining the relationships of current to voltage and current to resistance gives

I=VR.I=VR. size 12{I = { {V} over {R} } "."} {}
(3)

This relationship is also called Ohm’s law. Ohm’s law in this form really defines resistance for certain materials. Ohm’s law (like Hooke’s law) is not universally valid. The many substances for which Ohm’s law holds are called ohmic. These include good conductors like copper and aluminum, and some poor conductors under certain circumstances. Ohmic materials have a resistance RR size 12{R} {} that is independent of voltage VV size 12{V} {} and current II size 12{I} {}. An object that has simple resistance is called a resistor, even if its resistance is small. The unit for resistance is an ohm and is given the symbol ΩΩ size 12{ %OMEGA } {} (upper case Greek omega). Rearranging I=V/RI=V/R size 12{I = ital "V/R"} {} gives R=V/IR=V/I size 12{R= ital "V/I"} {}, and so the units of resistance are 1 ohm = 1 volt per ampere:

1 Ω= 1 VA.1 Ω= 1 VA. size 12{"1 " %OMEGA =" 1 " { {V} over {A} } "."} {}
(4)

Figure 1 shows the schematic for a simple circuit. A simple circuit has a single voltage source and a single resistor. The wires connecting the voltage source to the resistor can be assumed to have negligible resistance, or their resistance can be included in RR size 12{R} {}.

### Example 1: Calculating Resistance: An Automobile Headlight

What is the resistance of an automobile headlight through which 2.50 A flows when 12.0 V is applied to it?

Strategy

We can rearrange Ohm’s law as stated by I=V/RI=V/R size 12{I = ital "V/R"} {} and use it to find the resistance.

Solution

Rearranging I=V/RI=V/R size 12{I = ital "V/R"} {} and substituting known values gives

R=VI=12.0 V2.50 A= 4.80 Ω.R=VI=12.0 V2.50 A= 4.80 Ω. size 12{R = { {V} over {I} } = { {"12" "." "0 V"} over {2 "." "50 A"} } =" 4" "." "80 " %OMEGA "."} {}
(5)

Discussion

This is a relatively small resistance, but it is larger than the cold resistance of the headlight. As we shall see in Resistance and Resistivity, resistance usually increases with temperature, and so the bulb has a lower resistance when it is first switched on and will draw considerably more current during its brief warm-up period.

Resistances range over many orders of magnitude. Some ceramic insulators, such as those used to support power lines, have resistances of 1012Ω1012Ω size 12{"10" rSup { size 8{"12"} }  %OMEGA } {} or more. A dry person may have a hand-to-foot resistance of 105Ω105Ω size 12{"10" rSup { size 8{5} }  %OMEGA } {}, whereas the resistance of the human heart is about 103Ω103Ω size 12{"10" rSup { size 8{3} }  %OMEGA } {}. A meter-long piece of large-diameter copper wire may have a resistance of 105Ω105Ω size 12{"10" rSup { size 8{ - 5} }  %OMEGA } {}, and superconductors have no resistance at all (they are non-ohmic). Resistance is related to the shape of an object and the material of which it is composed, as will be seen in Resistance and Resistivity.

Additional insight is gained by solving I=V/RI=V/R size 12{I = ital "V/R"} {} for V,V, size 12{V} {} yielding

V=IR.V=IR. size 12{V = ital "IR."} {}
(6)

This expression for VV size 12{V} {} can be interpreted as the voltage drop across a resistor produced by the flow of current II size 12{I} {}. The phrase IRIR size 12{ ital "IR"} {} drop is often used for this voltage. For instance, the headlight in Example 1 has an IRIR size 12{ ital "IR"} {} drop of 12.0 V. If voltage is measured at various points in a circuit, it will be seen to increase at the voltage source and decrease at the resistor. Voltage is similar to fluid pressure. The voltage source is like a pump, creating a pressure difference, causing current—the flow of charge. The resistor is like a pipe that reduces pressure and limits flow because of its resistance. Conservation of energy has important consequences here. The voltage source supplies energy (causing an electric field and a current), and the resistor converts it to another form (such as thermal energy). In a simple circuit (one with a single simple resistor), the voltage supplied by the source equals the voltage drop across the resistor, since PE=qΔVPE=qΔV size 12{"PE"=qΔV} {}, and the same qq size 12{q} {} flows through each. Thus the energy supplied by the voltage source and the energy converted by the resistor are equal. (See Figure 2.)

### Making Connections: Conservation of Energy:

In a simple electrical circuit, the sole resistor converts energy supplied by the source into another form. Conservation of energy is evidenced here by the fact that all of the energy supplied by the source is converted to another form by the resistor alone. We will find that conservation of energy has other important applications in circuits and is a powerful tool in circuit analysis.

## PhET Explorations: Ohm's Law:

See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.

## Section Summary

• A simple circuit is one in which there is a single voltage source and a single resistance.
• One statement of Ohm’s law gives the relationship between current I I , voltage V V , and resistance R R in a simple circuit to be I=VR.I=VR. size 12{I = { {V} over {R} } } {}
• Resistance has units of ohms ( Ω Ω ), related to volts and amperes by 1 Ω= 1 V/A1 Ω= 1 V/A size 12{1 %OMEGA =" 1 V/A"} {}.
• There is a voltage or IRIR size 12{ ital "IR"} {} drop across a resistor, caused by the current flowing through it, given by V=IRV=IR size 12{V = ital "IR" } {}.

## Conceptual Questions

### Exercise 1

The IRIR size 12{ ital "IR"} {} drop across a resistor means that there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor? Explain.

### Exercise 2

How is the IRIR size 12{ ital "IR"} {} drop in a resistor similar to the pressure drop in a fluid flowing through a pipe?

## Problems & Exercises

### Exercise 1

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is 3.60 Ω3.60 Ω size 12{3 "." "60" %OMEGA } {}?

### Exercise 2

Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows.

### Exercise 3

What is the effective resistance of a car’s starter motor when 150 A flows through it as the car battery applies 11.0 V to the motor?

### Exercise 4

How many volts are supplied to operate an indicator light on a DVD player that has a resistance of 140 Ω140 Ω size 12{1"40 " %OMEGA } {}, given that 25.0 mA passes through it?

### Exercise 5

(a) Find the voltage drop in an extension cord having a 0.0600-Ω0.0600-Ω size 12{0 "." "0600-" %OMEGA } {} resistance and through which 5.00 A is flowing. (b) A cheaper cord utilizes thinner wire and has a resistance of 0.300Ω0.300Ω size 12{0 "." "300" %OMEGA } {}. What is the voltage drop in it when 5.00 A flows? (c) Why is the voltage to whatever appliance is being used reduced by this amount? What is the effect on the appliance?

### Exercise 6

A power transmission line is hung from metal towers with glass insulators having a resistance of 1.00×109Ω.1.00×109Ω. size 12{1 "." "00"´"10" rSup { size 8{9} } %OMEGA } {} What current flows through the insulator if the voltage is 200 kV? (Some high-voltage lines are DC.)

## Glossary

Ohm’s law:
an empirical relation stating that the current I is proportional to the potential difference V, ∝ V; it is often written as I = V/R, where R is the resistance
resistance:
the electric property that impedes current; for ohmic materials, it is the ratio of voltage to current, R = V/I
ohm:
the unit of resistance, given by 1Ω = 1 V/A
ohmic:
a type of a material for which Ohm's law is valid
simple circuit:
a circuit with a single voltage source and a single resistor

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

### Reuse / Edit:

Reuse or edit collection (?)

#### Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

#### Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.

| Reuse or edit module (?)

#### Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

#### Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.