PHYS 208 Lecture 12

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R.I.P. Steve Jobs

Exam 2 October 18, 7:30 PM

Chapter 26: DC Circuits

Resistors in Series

Current $I$ is constant; the same current flows through all components.

$V_{total}=\sum _{i}V_{i}=V_{1}+V_{2}+\dots$ $R_{eq}=\sum _{i}R_{i}=R_{1}+R_{2}+\dots$

Resistors in Parallel

Voltage $V$ is constant; the same potential is supplied to each component

$I_{total}=\sum _{i}I_{i}=I_{1}+I_{2}+\dots$ ${\frac {1}{R_{eq}}}=\sum _{i}{\frac {1}{R_{i}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\dots$

Multi-Loop Circuits: Kirchhoff's Laws

Based on Conservation of Charge and Conservation of Energy within a circuit

1. Junction Rule: Currents flowing into a junction = currents flowing out from that same junction
2. Loop Rule: sum of potential (V) around a circuit = 0

Conventions

• For resistors, potential difference V is
  • negative if your loop direction and current direction are the same
  • positive if your loop direction and current direction are opposite
• For batteries, potential difference V is
  • positive if your loop direction and current direction are the same
  • negative if your loop direction and current direction are opposite

Problem-Solving Strategies

1. Label the terminals of the battery
2. Choose the direction of the currents you will be using, and label them clearly (can be done arbitrarily; if your current result is negative, then current is really flowing the other way)
3. Apply Kirchhoff’s Junction Rule at one or more junctions in the circuit.
4. Choose the paths and directions for the loops that you will consider in the circuit.
5. Apply Kirchhoff’s Loop Rule around one or more loops, remembering to use current direction conventions.
6. Solve equations algebraically for unknown variables.