🔖 Topics

  • Conventional current
  • Ohm's law
  • Power dissipated in a resistor
  • Resistivity
  • Resistors in series
  • Resistors in parallel

🎯 Objectives

  • Calculate the current and voltage across an ideal resistor connected to an ideal battery
  • Calculate the power dissipated in a resistor that has some constant current flowing through it
  • Calculate the resistance of a resistor given its geometric properties and material resistivity
  • Calculate the equivalent resistance of many resistors in a circuit

📋 Sequence

  • Conventional current
  • Review of Ohm’s law: \( V = IR \)
  • Power dissipated in a resistor: \( P = IV \)
  • Resistance of a resistor: \( R = \rho l / A \)
  • Resistors in series
  • Resistors in parallel
  • Comparison of series and parallel to capacitors
  • Qualitative argument of why series / parallel have the forms that they do

🖥️ Animations, Simulations, Activities

📝 Practice Problems

Resistors

  1. A resistor with a resistance of \( R = 250 \: \Omega \) is connected to a 9 volt battery. What is the current drawn from the battery? What is the power dissipated across the resistor?
  2. Four resistors, each with a resistance of \( 10 \: \Omega \) are connected in series along a voltage source of \( V = 25 \: V \). What is the power dissipated in each resistor? What is the total power dissipated in the circuit?
  3. Four resistors, each with a resistance of \( 10 \: \Omega \) are connected in parallel along a voltage source of \( V = 25 \: V \). What is the power dissipated in each resistor? What is the total power dissipated in the circuit?

  4. What is the equivalent resistance between nodes (a) and (d) in the diagram below? You can assume that each resistor is \( R = 1 \: \Omega \).

    Resistor Network 1

  5. What is the net current being drawn from the battery in the diagram below? The battery has a voltage of 3 V.

    Resistor Network 2

✅ Partial Solutions

  1. I = 36 mA; P = 0.324 W
  2. 3.9 W; 15.6 W
  3. 62.5 W; 250 W
  4. \( 1.38 \: \Omega \)
  5. 1 A

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.
  • Rouinfar, Amy, et al. “Circuit Construction Kit: DC.” PhET, https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuit-construction-kit-dc_en.html, January 2024.