AP Physics C: Electricity and Magnetism
Direct Current Circuits
Electric Circuits
Learning Objectives
By the end of this lesson, students should be able to:
-
Define an electric circuit.
-
Identify the essential components of a circuit.
-
Understand how charge moves in a complete circuit.
-
Distinguish between open and closed circuits.
-
Explain the role of batteries and circuit elements.
-
Apply conservation of charge and energy to electric circuits.
-
Analyze simple direct current (DC) circuits.
Introduction to Electric Circuits
What is an Electric Circuit?
An electric circuit is a closed conducting path through which electric charge can flow continuously.
A circuit provides a complete loop that allows charge carriers to move from one location and eventually return to their starting point.
Without a complete path, continuous current cannot exist.
Why Circuits Matter
Electric circuits are fundamental to modern technology.
Examples include:
-
Flashlights
-
Smartphones
-
Computers
-
Automobiles
-
Household electrical systems
Understanding circuits is essential for studying current, resistance, power, and electrical energy.
Essential Components of a Circuit
Source of Electrical Energy
Every functioning circuit requires an energy source.
Common examples include:
-
Batteries
-
Power supplies
-
Generators
The source provides electrical energy that drives charge through the circuit.
Conducting Path
Charges must have a path through which they can move.
Conducting paths are usually made from:
-
Copper wires
-
Aluminum wires
-
Metal connectors
These conductors provide low-resistance pathways for current.
Load
A load is a device that converts electrical energy into another form of energy.
Examples include:
-
Light bulbs
-
Motors
-
Heaters
-
Speakers
The load uses electrical energy supplied by the source.
Switch
A switch controls whether the circuit is complete.
When the switch is closed:
-
Current flows.
When the switch is open:
-
Current stops.
Closed Circuits
Complete Path
A closed circuit provides an uninterrupted conducting loop.
Current can flow continuously because charge has a complete path.
Example:
Battery → Wire → Light Bulb → Wire → Battery
Current Flow
In a closed circuit:
$$
I\neq0
$$
Charges move through every part of the circuit.
The current is established almost immediately throughout the circuit when the switch is closed.
Open Circuits
Broken Path
An open circuit contains a gap somewhere in the conducting path.
Examples:
-
Open switch
-
Broken wire
-
Burned-out component
Because the path is incomplete, current cannot flow.
Current in an Open Circuit
For an open circuit:
$$
I=0
$$
No continuous charge flow exists.
The Role of the Battery
Energy Source
A battery does not create charge.
Instead, it supplies energy to existing charges in the circuit.
The battery performs work on charges and increases their electrical potential energy.
Potential Difference
The battery establishes a potential difference:
$$
\Delta V
$$
between its terminals.
This potential difference drives charge through the circuit.
The larger the potential difference, the greater the ability to move charge.
Charge Motion in a Circuit
What Actually Moves?
In metallic conductors:
-
Electrons are the charge carriers.
-
Electrons move through the conductor.
However, conventional current is defined as the direction positive charge would move.
Conventional Current
Conventional current flows:
-
Out of the positive terminal
-
Through the external circuit
-
Into the negative terminal
This convention is used throughout circuit analysis.
Electron Flow
Electron flow occurs in the opposite direction:
-
Out of the negative terminal
-
Toward the positive terminal
AP Physics circuit equations use conventional current.
Conservation of Charge
Charge Does Not Disappear
Charge is conserved throughout a circuit.
The amount of charge entering any junction must equal the amount leaving.
Mathematically:
$$
\sum I_{in}=\sum I_{out}
$$
This principle forms the basis of Kirchhoff’s Junction Rule.
Physical Interpretation
Charges do not accumulate indefinitely at any point in a circuit.
The current entering a junction must equal the current leaving.
Conservation of Energy
Energy Transfer in Circuits
Energy is conserved as charges move through a circuit.
The battery provides energy.
Circuit elements consume or transform that energy.
Loop Rule Concept
Around a complete circuit loop:
$$
\sum \Delta V = 0
$$
This idea becomes Kirchhoff’s Loop Rule.
The total energy gained equals the total energy lost.
Series Circuits
Definition
A series circuit contains only one path for current.
Example:
Battery → Resistor → Light Bulb → Battery
Current in Series
Because there is only one path:
$$
I_1=I_2=I_3
$$
The same current flows through every component.
Characteristics
Series circuits:
-
Have a single path.
-
Share the same current.
-
Stop functioning if one component fails.
Parallel Circuits
Definition
A parallel circuit contains multiple paths for current.
Charges can choose different branches.
Current in Parallel
At a junction:
$$
I_{total}=I_1+I_2+I_3
$$
Current divides among the branches.
Characteristics
Parallel circuits:
-
Provide multiple current paths.
-
Allow independent operation of components.
-
Continue functioning if one branch fails.
Circuit Diagrams
Standard Symbols
Common circuit symbols include:
Battery
$$
| ; |
$$
Resistor
$$
\text{zigzag line}
$$
Switch
$$
\text{open or closed break}
$$
Wire
$$
\text{straight line}
$$
AP Physics students should become familiar with these standard symbols.
Example 1
Charge Passing Through a Circuit
A current of
$$
4.0A
$$
flows for
$$
15s
$$
How much charge passes through the circuit?
Solution
Use:
$$
Q=It
$$
Substitute:
$$
Q=(4.0)(15)
$$
$$
Q=60C
$$
Answer
$$
Q=60C
$$
Example 2
Current at a Junction
A current of
$$
8A
$$
enters a junction.
One branch carries:
$$
3A
$$
Find the current in the second branch.
Solution
Apply charge conservation:
$$
I_{in}=I_{out}
$$
$$
8=3+I
$$
$$
I=5A
$$
Answer
$$
I=5A
$$
Example 3
Closed vs Open Circuit
A battery is connected to a light bulb through a switch.
The switch is open.
Determine the current.
Solution
An open switch creates an open circuit.
Therefore:
$$
I=0
$$
Answer
$$
I=0A
$$
No current flows.
Common AP Exam Mistakes
Mistake 1
Believing that batteries supply charge.
Batteries supply energy, not charge.
The charges already exist in the conducting wires.
Mistake 2
Confusing current and energy.
Current measures charge flow.
Energy measures the ability to do work.
They are different physical quantities.
Mistake 3
Ignoring conservation laws.
Always remember:
Charge Conservation:
$$
\sum I_{in}=\sum I_{out}
$$
Energy Conservation:
$$
\sum \Delta V = 0
$$
AP Free-Response Strategy
Identify Circuit Type
Determine whether the circuit is:
-
Series
-
Parallel
-
Combination
This often determines the solution method immediately.
Apply Conservation Principles
Nearly every circuit problem uses:
Charge conservation
$$
\sum I_{in}=\sum I_{out}
$$
or
Energy conservation
$$
\sum \Delta V = 0
$$
Draw Current Directions
Clearly label current directions before writing equations.
This reduces sign errors and improves organization.
Summary
Key Takeaways
-
An electric circuit is a complete conducting path for charge flow.
-
A functioning circuit requires:
-
Energy source
-
Conducting path
-
Load
-
Complete loop
-
-
Closed circuits allow current flow.
$$
I\neq0
$$
-
Open circuits prevent current flow.
$$
I=0
$$
-
Batteries provide energy through a potential difference.
$$
\Delta V
$$
-
Charge is conserved.
$$
\sum I_{in}=\sum I_{out}
$$
-
Energy is conserved.
$$
\sum \Delta V = 0
$$
-
Series circuits share the same current.
-
Parallel circuits divide current among branches.
-
Electric circuits form the foundation for understanding resistance, Ohm’s Law, power, and advanced circuit analysis in AP Physics C.