Rucete ✏ AP Physics 2 In a Nutshell
2. Steady-State Circuits
This chapter explores electric circuits under steady-state conditions, focusing on current, resistance, electric power, series and parallel circuits, Kirchhoff’s rules, capacitors in circuits, and the role of electrical potential energy.
Current and Electricity
• Electric current (I) is the flow of charge per unit time: I = Δq/Δt (units: amperes, A).
• Conventional current flows from positive to negative terminal.
• A battery provides the electromotive force (emf), maintaining a continuous flow of charges.
• Voltage is the potential difference that drives the current.
Electric Resistance
• Resistance (R) opposes the flow of current, causing energy loss as heat.
• Ohm’s law: V = IR (for Ohmic materials at constant temperature).
• Resistance depends on material resistivity (ρ), length (L), and cross-sectional area (A): R = ρ(L/A)
• Materials with low resistivity (e.g., silver, copper) are good conductors; high resistivity materials are good insulators.
Electric Power and Energy
• Electrical power: P = IV = I²R = V²/R
• Units: watts (W); energy = power × time.
• Energy is transferred when electric current does work, such as lighting a bulb or running a motor.
• Appliances typically operate at constant voltage (e.g., 120 V in the U.S.).
Kirchhoff’s Rules
• Junction rule: total current into a junction equals total current out (conservation of charge).
• Loop rule: sum of voltage gains and drops around a closed loop equals zero (conservation of energy).
• Resistors in a loop contribute voltage drops; batteries contribute voltage gains.
Series Circuits
• Same current flows through each resistor.
• Total resistance: Req = R₁ + R₂ + R₃ + ...
• Voltage divides across resistors proportionally to their resistances.
• If one component fails, the entire circuit is broken.
Parallel Circuits
• Same voltage across each branch.
• Total resistance: 1/Req = 1/R₁ + 1/R₂ + 1/R₃ + ...
• Currents divide among branches inversely proportional to resistance.
• If one component fails, other branches continue functioning.
Combination Circuits
• Circuits often combine series and parallel elements.
• Simplify step-by-step: reduce parallel and series sections separately.
• Apply Ohm’s law and Kirchhoff’s rules to find unknown currents, voltages, and resistances.
Capacitors in Circuits
In Series
• Reciprocal addition: 1/Ceq = 1/C₁ + 1/C₂ + 1/C₃ + ...
• Charge on each capacitor is the same.
• Voltage divides among capacitors.
In Parallel
• Direct addition: Ceq = C₁ + C₂ + C₃ + ...
• Voltage across each capacitor is the same.
• Total stored charge is the sum of individual charges.
In a Nutshell
Steady-state circuits maintain constant currents and voltages governed by Ohm’s law and Kirchhoff’s rules. Understanding series and parallel configurations helps predict behavior of complex networks. Capacitors store energy and combine differently than resistors. Mastering these basics enables analysis of electrical systems from simple lights to complex electronics.