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 $V$ 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 $V$ 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*:

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 $R$. 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

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

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 $R$ that is independent of voltage $V$ and current $I$. 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 $\Omega $ (upper case Greek omega). Rearranging $I=\text{V/R}$ gives $R=\text{V/I}$, and so the units of resistance are 1 ohm = 1 volt per ampere:

[link] 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 $R$.

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 $I=\text{V/R}$ and use it to find the resistance.

**Solution**

Rearranging $I=\text{V/R}$ and substituting known values gives

**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 ${\text{10}}^{\text{12}}\phantom{\rule{0.25em}{0ex}}\Omega $ or more. A dry person may have a hand-to-foot resistance of ${\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\Omega $, whereas the resistance of the human heart is about ${\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\Omega $. A meter-long piece of large-diameter copper wire may have a resistance of ${\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\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 $I=\text{V/R}$ for $V,\phantom{\rule{0.25}{0ex}}$ yielding

This expression for $V$ can be interpreted as the *voltage drop across a resistor produced by the flow of current *$I$. The phrase $\text{IR}$ * drop* is often used for this voltage. For instance, the headlight in [link] has an $\text{IR}$ 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 $\text{PE}=q\mathrm{\Delta}V$, and the same $q$ flows through each. Thus the energy supplied by the voltage source and the energy converted by the resistor are equal. (See [link].)

# 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 $I$, voltage $V$, and resistance $R$ in a simple circuit to be $I=\frac{V}{R}.$
- Resistance has units of ohms ($\text{\Omega}$), related to volts and amperes by $\mathrm{1\; \Omega}=\text{1 V/A}$.
- There is a voltage or $\text{IR}$ drop across a resistor, caused by the current flowing through it, given by $V=\text{IR}$.

# Conceptual Questions

The $\text{IR}$ 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.

How is the $\text{IR}$ drop in a resistor similar to the pressure drop in a fluid flowing through a pipe?

# Problems & Exercises

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is $3\text{.}\text{60 \Omega}$?

0.833 A

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

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?

$7\text{.}\text{33}\times {\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\Omega $

How many volts are supplied to operate an indicator light on a DVD player that has a resistance of $1\text{40}\phantom{\rule{0.25em}{0ex}}\Omega $, given that 25.0 mA passes through it?

(a) Find the voltage drop in an extension cord having a $0\text{.}\text{0600-}\Omega $ resistance and through which 5.00 A is flowing. (b) A cheaper cord utilizes thinner wire and has a resistance of $0\text{.}\text{300}\phantom{\rule{0.25em}{0ex}}\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?

(a) 0.300 V

(b) 1.50 V

(c) The voltage supplied to whatever appliance is being used is reduced because the total voltage drop from the wall to the final output of the appliance is fixed. Thus, if the voltage drop across the extension cord is large, the voltage drop across the appliance is significantly decreased, so the power output by the appliance can be significantly decreased, reducing the ability of the appliance to work properly.

A power transmission line is hung from metal towers with glass insulators having a resistance of $1\text{.}\text{00}\times {\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\Omega .$ What current flows through the insulator if the voltage is 200 kV? (Some high-voltage lines are DC.)

### Tập tin đính kèm

- ohms-law_en.jar

- College Physics
- Preface
- Introduction: The Nature of Science and Physics
- Kinematics
- Introduction to One-Dimensional Kinematics
- Displacement
- Vectors, Scalars, and Coordinate Systems
- Time, Velocity, and Speed
- Acceleration
- Motion Equations for Constant Acceleration in One Dimension
- Problem-Solving Basics for One-Dimensional Kinematics
- Falling Objects
- Graphical Analysis of One-Dimensional Motion

- Two-Dimensional Kinematics
- Dynamics: Force and Newton's Laws of Motion
- Introduction to Dynamics: Newton’s Laws of Motion
- Development of Force Concept
- Newton’s First Law of Motion: Inertia
- Newton’s Second Law of Motion: Concept of a System
- Newton’s Third Law of Motion: Symmetry in Forces
- Normal, Tension, and Other Examples of Forces
- Problem-Solving Strategies
- Further Applications of Newton’s Laws of Motion
- Extended Topic: The Four Basic Forces—An Introduction

- Further Applications of Newton's Laws: Friction, Drag, and Elasticity
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- Introduction to Rotational Motion and Angular Momentum
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- Dynamics of Rotational Motion: Rotational Inertia
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- Angular Momentum and Its Conservation
- Collisions of Extended Bodies in Two Dimensions
- Gyroscopic Effects: Vector Aspects of Angular Momentum

- Fluid Statics
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- Introduction to Fluid Dynamics and Its Biological and Medical Applications
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- Bernoulli’s Equation
- The Most General Applications of Bernoulli’s Equation
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- The Onset of Turbulence
- Motion of an Object in a Viscous Fluid
- Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

- Temperature, Kinetic Theory, and the Gas Laws
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- Thermodynamics
- Introduction to Thermodynamics
- The First Law of Thermodynamics
- The First Law of Thermodynamics and Some Simple Processes
- Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency
- Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated
- Applications of Thermodynamics: Heat Pumps and Refrigerators
- Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy
- Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

- Oscillatory Motion and Waves
- Introduction to Oscillatory Motion and Waves
- Hooke’s Law: Stress and Strain Revisited
- Period and Frequency in Oscillations
- Simple Harmonic Motion: A Special Periodic Motion
- The Simple Pendulum
- Energy and the Simple Harmonic Oscillator
- Uniform Circular Motion and Simple Harmonic Motion
- Damped Harmonic Motion
- Forced Oscillations and Resonance
- Waves
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- Energy in Waves: Intensity

- Physics of Hearing
- Electric Charge and Electric Field
- Introduction to Electric Charge and Electric Field
- Static Electricity and Charge: Conservation of Charge
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- Coulomb’s Law
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- Electric Field Lines: Multiple Charges
- Electric Forces in Biology
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- Applications of Electrostatics

- Electric Potential and Electric Field
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- Circuits, Bioelectricity, and DC Instruments
- Magnetism
- Introduction to Magnetism
- Magnets
- Ferromagnets and Electromagnets
- Magnetic Fields and Magnetic Field Lines
- Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field
- Force on a Moving Charge in a Magnetic Field: Examples and Applications
- The Hall Effect
- Magnetic Force on a Current-Carrying Conductor
- Torque on a Current Loop: Motors and Meters
- Magnetic Fields Produced by Currents: Ampere’s Law
- Magnetic Force between Two Parallel Conductors
- More Applications of Magnetism

- Electromagnetic Induction, AC Circuits, and Electrical Technologies
- Introduction to Electromagnetic Induction, AC Circuits and Electrical Technologies
- Induced Emf and Magnetic Flux
- Faraday’s Law of Induction: Lenz’s Law
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- Eddy Currents and Magnetic Damping
- Electric Generators
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- Transformers
- Electrical Safety: Systems and Devices
- Inductance
- RL Circuits
- Reactance, Inductive and Capacitive
- RLC Series AC Circuits

- Electromagnetic Waves
- Geometric Optics
- Vision and Optical Instruments
- Wave Optics
- Introduction to Wave Optics
- The Wave Aspect of Light: Interference
- Huygens's Principle: Diffraction
- Young’s Double Slit Experiment
- Multiple Slit Diffraction
- Single Slit Diffraction
- Limits of Resolution: The Rayleigh Criterion
- Thin Film Interference
- Polarization
- *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light

- Special Relativity
- Introduction to Quantum Physics
- Atomic Physics
- Introduction to Atomic Physics
- Discovery of the Atom
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- Bohr’s Theory of the Hydrogen Atom
- X Rays: Atomic Origins and Applications
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- Quantum Numbers and Rules
- The Pauli Exclusion Principle

- Radioactivity and Nuclear Physics
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