#AP Physics C: E&M - Resistance, Ohm's Law, and Circuit Elements ⚡

Hey, future physicist! Let's get you prepped for the AP exam with a super-focused review of resistance, Ohm's Law, and circuit elements. This is your go-to guide for a quick, effective study session the night before the test.

#Foundational Concepts: Resistance and Ohm's Law

These are the building blocks of circuit analysis. Understanding them is key to tackling more complex problems. Let's dive in!

#Ohm's Law

Definition: Ohm's Law describes the relationship between voltage ( $V$ ), current ( $I$ ), and resistance ( $R$ ) in a circuit: $V = IR$

Key Concept

This equation is your bread and butter! Remember it well, as it's used in almost every circuit problem.

Voltage ( $V$ ): The electrical potential difference across a component, measured in volts (V).
Current ( $I$ ): The flow of electric charge, measured in amperes (A).
Resistance ( $R$ ): The opposition to the flow of current, measured in ohms (Ω).

#Resistivity

Definition: Resistivity ( $ho$ ) is a material's intrinsic property that measures how strongly it opposes the flow of electric current. It's measured in ohm-meters (Ω⋅m).
Key Point: Unlike resistance, which depends on the dimensions of the material, resistivity is a property of the material itself.

#Resistance

Definition: Resistance ( $R$ ) is the measure of how much a material opposes the flow of electric current. It depends on the material's resistivity ( $ho$ ), length ( $L$ ), and cross-sectional area ( $A$ ): $R = \frac{\rho L}{A}$

Memory Aid

Think of it like this: a long, skinny wire (high $L$ , small $A$ ) will have more resistance than a short, thick wire (small $L$ , high $A$ ).

#Electrical Characteristics of Circuit Elements

#Ohm's Law in Circuits

The Relationship: Ohm's Law ( $V = IR$ ) relates current, resistance, and potential difference across a conductive element in a circuit. 🔌

Quick Fact

Remember: Voltage is like the push, current is the flow, and resistance is the opposition.

Common Mistake

Ohmic Materials:
- Have constant resistance regardless of current.
- Their $I$ - $V$ graph is a straight line.
- Resistivity ( $ho$ ) remains constant, even with temperature changes (within reasonable limits).
Resistors:
- Convert electrical energy into thermal energy.
- This conversion can change the temperature of the resistor and its surroundings.
- Example: A light bulb filament heats up and glows when current flows through it.
Determining Resistance:
- The resistance of an ohmic element is the slope of its $I$ - $V$ graph.
- A steeper slope indicates higher resistance, and a flatter slope indicates lower resistance.

Don't confuse resistance and resistivity! Resistance depends on the size and shape of the material, while resistivity is an inherent property of the material.

🚫 Boundary Statements:

On the AP exam, you only need to focus on the transfer of mechanical and electrical energy. However, you should also know that electrical energy can be dissipated as thermal energy.

Practice Question

Multiple Choice Questions

A cylindrical wire has a resistance R. If the length of the wire is doubled and the radius is halved, the new resistance will be: (A) R/4 (B) R/2 (C) R (D) 4R (E) 8R
A 12-V battery is connected to a resistor. If the current in the circuit is 2 A, what is the resistance of the resistor? (A) 6 Ω (B) 10 Ω (C) 14 Ω (D) 24 Ω (E) 30 Ω

Free Response Question

A student is investigating the properties of a new material. They create a cylindrical sample of the material with a length of 0.5 m and a radius of 0.01 m. They apply a voltage across the sample and measure the current. The following data is collected:

Voltage (V)	Current (A)
1.0	0.2
2.0	0.4
3.0	0.6
4.0	0.8

(a) Plot the current as a function of voltage on the graph below.

(b) Calculate the resistance of the material sample.

(d) If the length of the material is doubled and the radius is halved, what is the new resistance?

Scoring Guide

(a) (2 points)

1 point for correctly labeling axes and units
1 point for plotting the data accurately

(b) (2 points)

1 point for calculating the slope of the graph (resistance)
1 point for the correct value of the resistance (5 Ω)

1 point for using the correct formula: $R = \frac{\rho L}{A}$
1 point for calculating the area of the sample: $A = \pi r^2$
1 point for the correct value of the resistivity (approximately 3.14 x 10^-4 Ω⋅m)

(d) (3 points)

1 point for understanding the relationship between resistance, length, and area
1 point for doubling the length and halving the radius
1 point for calculating the new resistance (20 Ω)

#Final Exam Focus

#High-Priority Topics

Ohm's Law ( $V = IR$ ): Absolutely crucial for solving circuit problems.
Resistance and Resistivity: Understand the difference and how they relate to material properties and dimensions.
Energy Dissipation: Know that resistors convert electrical energy to thermal energy.

These topics are foundational and appear in almost every exam. Master them!

#Common Question Types

Circuit Analysis: Applying Ohm's Law to solve for current, voltage, or resistance in simple circuits.
Material Properties: Calculating resistance based on resistivity, length, and cross-sectional area.
Graphical Analysis: Interpreting $I$ - $V$ graphs to determine resistance.

#Last-Minute Tips

Time Management: Don't spend too long on a single problem. If you're stuck, move on and come back later.
Units: Always include units in your answers, and make sure they're consistent throughout your calculations.
Show Your Work: Even if you get the wrong answer, you can get partial credit for showing your steps.
Stay Calm: Take deep breaths and trust your preparation. You've got this!

Exam Tip

Remember to double-check your calculations and make sure your answers make sense in the context of the problem.

Good luck on your exam! You're going to do great! 💪