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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I} is constant; the same current flows through all components.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{total} = \sum_i V_i = V_1 + V_2 + \dots} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_{eq} = \sum_i R_i = R_1 + R_2 + \dots}

Resistors in Parallel

Voltage Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} is constant; the same potential is supplied to each component

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_{total} = \sum_i I_i = I_1 + I_2 + \dots} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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.