AP Physics C: Electricity and Magnetism

Direct Current Circuits

Electric Current

Learning Objectives

By the end of this lesson, students should be able to:

• Define electric current.

• Distinguish between conventional current and electron flow.

• Calculate current using charge and time.

• Understand current at the microscopic level.

• Apply current concepts to circuit analysis.

• Solve AP Physics C problems involving electric current.

Introduction to Electric Current

What is Electric Current?

Electric current is the rate at which electric charge flows through a conductor.

Whenever charges move through a wire or other conducting material, an electric current exists.

Electric current is represented by:

$$
I
$$

The SI unit of current is the ampere (A).

Definition of One Ampere

One ampere is defined as:

$$
1A=1\frac{C}{s}
$$

This means that one coulomb of charge passes through a cross-sectional area every second.

Definition of Electric Current

Current Equation

Electric current is defined as the amount of charge passing a point per unit time.

Mathematically:

$$
I=\frac{\Delta Q}{\Delta t}
$$

where:

• (I) = current

• (\Delta Q) = charge transferred

• (\Delta t) = time interval

Instantaneous Current

If the current changes with time, the instantaneous current is:

$$
I=\frac{dQ}{dt}
$$

This form is commonly used in calculus-based AP Physics C problems.

Conventional Current

Historical Definition

Before electrons were discovered, scientists defined current as the direction positive charge would move.

This convention remains in use today.

Conventional current flows:

• From positive terminal

• Toward negative terminal

Electron Flow

Electrons are negatively charged.

Therefore, electrons actually move:

• From negative terminal

• Toward positive terminal

Electron flow is opposite the direction of conventional current.

Important AP Exam Note

When solving circuit problems:

Always use conventional current unless otherwise specified.

Most circuit equations are based on conventional current direction.

Current in Conductors

Motion of Electrons

Inside a conductor:

• Free electrons move randomly.

• In the absence of an electric field, there is no net current.

When an electric field is applied:

• Electrons acquire a net drift motion.

• A current is established.

Drift Velocity

The average velocity of charge carriers is called the drift velocity.

It is represented by:

$$
v_d
$$

Although individual electrons move slowly, electrical signals propagate through circuits very rapidly.

Microscopic Model of Current

Charge Carriers

Current results from the motion of charge carriers.

Examples:

• Electrons in metals

• Ions in solutions

• Electrons and holes in semiconductors

For metallic conductors, electrons are the primary charge carriers.

Current and Drift Velocity

Current can be expressed as:

$$
I=nqAv_d
$$

where:

• (n) = number of charge carriers per unit volume

• (q) = charge of each carrier

• (A) = cross-sectional area

• (v_d) = drift velocity

Interpretation

The equation shows that current increases when:

• More charge carriers are present.

• The conductor is wider.

• Charge carriers move faster.

Current Density

Definition

Current density measures the amount of current flowing through a unit area.

It is defined as:

$$
J=\frac{I}{A}
$$

where:

• (J) = current density

• (I) = current

• (A) = cross-sectional area

Microscopic Form

Current density may also be written as:

$$
J=nqv_d
$$

This equation links microscopic particle motion to macroscopic current.

Charge Conservation in Circuits

Junction Rule

Charge is conserved in electrical circuits.

At any junction:

$$
\sum I_{in}=\sum I_{out}
$$

This principle later becomes Kirchhoff’s Junction Rule.

Physical Meaning

Charge cannot accumulate indefinitely at a junction.

The amount of charge entering must equal the amount leaving.

This idea is fundamental to circuit analysis.

Current and Electric Field

Relationship

An electric field inside a conductor causes charges to move.

The stronger the electric field:

• The greater the drift velocity.

• The larger the current.

This relationship leads directly to Ohm’s Law, which will be studied later.

Example 1

Finding Current

A wire carries:

$$
Q=12C
$$

of charge in:

$$
t=4.0s
$$

Find the current.

Solution

Use:

$$
I=\frac{\Delta Q}{\Delta t}
$$

Substitute values:

$$
I=\frac{12}{4.0}
$$

$$
I=3.0A
$$

Answer

$$
I=3.0A
$$

Example 2

Finding Charge

A current of:

$$
I=5.0A
$$

flows for:

$$
t=20s
$$

Find the charge transferred.

Solution

Rearrange:

$$
I=\frac{Q}{t}
$$

to obtain:

$$
Q=It
$$

Substitute:

$$
Q=(5.0)(20)
$$

$$
Q=100C
$$

Answer

$$
Q=100C
$$

Example 3

Number of Electrons Passing a Point

A current of:

$$
I=2.0A
$$

flows for:

$$
10s
$$

Find the number of electrons passing a point.

Solution

First calculate total charge:

$$
Q=It
$$

$$
Q=(2.0)(10)
$$

$$
Q=20C
$$

Each electron has charge:

$$
e=1.60\times10^{-19}C
$$

Number of electrons:

$$
N=\frac{Q}{e}
$$

$$
N=
\frac{20}
{1.60\times10^{-19}}
$$

$$
N=1.25\times10^{20}
$$

Answer

$$
N=1.25\times10^{20}
\text{ electrons}
$$

Common AP Exam Mistakes

Mistake 1

Confusing current and charge.

Current:

$$
I
$$

Charge:

$$
Q
$$

They represent different physical quantities.

Mistake 2

Using electron flow instead of conventional current.

Remember:

Circuit diagrams use conventional current direction.

Mistake 3

Forgetting units.

Current:

$$
A
$$

Charge:

$$
C
$$

Time:

$$
s
$$

Always verify dimensional consistency.

AP Free-Response Strategy

Start with Definitions

Many current problems begin with:

$$
I=\frac{\Delta Q}{\Delta t}
$$

Write this equation immediately.

It often earns partial credit.

Use Charge Conservation

At circuit junctions:

$$
\sum I_{in}=\sum I_{out}
$$

This principle appears frequently in AP circuit problems.

Identify What is Asked

Determine whether the problem asks for:

• Current

• Charge

• Time

• Number of electrons

Then choose the appropriate equation.

Summary

Key Takeaways

• Electric current is the rate of charge flow.

$$
I=\frac{\Delta Q}{\Delta t}
$$

• Instantaneous current is:

$$
I=\frac{dQ}{dt}
$$

• One ampere equals one coulomb per second.

$$
1A=1\frac{C}{s}
$$

• Conventional current flows from positive to negative.

• Electron flow is opposite conventional current.

• Current can be expressed microscopically as:

$$
I=nqAv_d
$$

• Current density is:

$$
J=\frac{I}{A}
$$

• Charge conservation requires:

$$
\sum I_{in}=\sum I_{out}
$$

• Electric current is the foundation for understanding resistance, Ohm’s Law, and all direct current circuits.