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Chapter 20: Electrodynamics

20.B: Electric Circuits

Open Circuit: A circuit that does not have a complete path, preventing current from flowing.
Closed Circuit: A complete circuit path where current can flow.
Series Circuit: A circuit with a single path for current flow.
Parallel Circuit: A circuit with multiple paths for current flow.
Equivalent Resistance: The total resistance of a series or parallel circuit that could replace all resistors without altering current or voltage.

Series Circuits

Current remains constant throughout the circuit.
Voltage drops across each component add up to the total voltage: $V_{total} = V_{1} + V_{2} + V_{n}$
Total resistance is the sum of individual resistances: $R_{total} = R_{1} + R_{2} + R_{n}$

Parallel Circuits

Voltage is the same across all branches.
Total current is the sum of the branch currents: $I_{total} = I_{1} + I_{2} + I_{n}$
Total resistance is given by: $\frac{1}{R_{total}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{n}}$

Kirchhoff's Laws

Kirchhoff's Voltage Law (KVL): The sum of voltage changes around a closed loop equals zero.
Kirchhoff's Current Law (KCL): The sum of currents entering a node equals the sum of currents leaving the node.

Applications

Household Wiring: Uses parallel circuits for consistent voltage across devices.
Christmas Lights: Older lights used series circuits; modern designs use parallel branches.

Questions for Students

Define open and closed circuits with examples.
Explain the difference between series and parallel circuits.
Calculate the equivalent resistance of a series circuit with resistors of 10 Ω, 20 Ω, and 30 Ω.
State and apply Kirchhoff's Voltage and Current Laws.
Why does adding resistors in parallel decrease total resistance?