Chapter 4 - Electric Circuits

Current

  • __Current__: the amount of charge passing a point in a given time period   * ==I = ΔQ/Δt==     * I: current (Amperes)     * Q: charge (Coulombs)     * t: time (seconds)   * Current is described in the AP exam as the flow of positive charge

Ohm’s Law

  • __Batteries__: create currents using a difference in potential   * The “+” terminal has a higher electric potential   * The “-” terminal has a lower electric potential   * Generally, the greater the potential difference, the more current flows
  • __Resistance__: a property of the circuit that resists the current   * Units are Ohms (Ω)   * ==R = ⍴L/A==     * R: resistance     * ⍴: resistivity     * L: length of wire     * A: cross-sectional area of wire
  • Ohm’s Law   * ==I = ΔV/R==     * ΔV: voltage across a certain part of the circuit (like a resistor)     * R: resistance     * I: current
  • Power: the rate at which electrical energy is converted to heat energy   * ==P = IΔV = I^2 R = ΔV^2/R==
  • Ohmic vs. Nonohmic   * Ohmic: a circuit part (resistor or capacitor) that maintains the same resistance when the voltage across it or current through it changes - resistance is constant
  • Circuit Pictures   * Wire: straight line   * Battery: 4 parallel lines - one long line and then one smaller line repeated   * Resistor: zig zag line   * Capacitor: 2 parallel lines
  • Resistors in Series   * ==R = ⅀Ri==     * Ri: the resistances of the resistors in series with each other     * R: equivalent resistance or total resistance
  • Resistors in Parallel   * ==1/R = ⅀1/Ri==     * Ri: the resistances of the resistors in parallel with each other     * R: equivalent resistance or total resistance
  • Rules for resistors in circuits   * The current in resistors in series is equal to each other   * The voltage across resistors in parallel is equal to each other     * The voltage across two resistors in parallel is also equal to the voltage across each individual resistor
  • V-I-R charts   * Create columns of V, I, and R for each individual resistor and the total circuit   * This helps us stay organized in complex problems

Kirchhoff’s Rules

  • __Junction Rule__: The current entering and leaving a junction is equal
  • __Loop Rule__: In a closed loop, the sum of the voltages is 0   * Choose a loop of the circuit and when you see a resistor, the voltage is -IR because resistors resist the current   * If the loop is against the current, the voltage is +IR   * When you see a batter, add the voltage of the battery (if going from - to +)     * If you go from + to -, subtract the voltage of the battery   * If the current you calculate is negative, you chose the wrong direction and the current flows the opposite way

Experimental Circuits

  • In calculations, we assume most electronic devices in circuits act as resistors
  • Light bulb   * The brightness of a bulb depends only on the power dissipated   * The power of a bulb can change depending on the current and voltage of the circuit it’s in
  • Ammeters and Voltmeters   * Ammeters: measure current     * Ammeters work by putting them in series with resistors (current is constant for resistors in series)   * Voltmeters: measure potential difference (voltage)     * Voltmeters work by putting them parallel to parallel resistors
  • Real batteries   * In a perfect world, batteries have no resistance but in the real world, this is not true   * The voltage advertised by a battery, ε, is actually larger than the real voltage ΔV (terminal voltage)     * ==ΔV = ε - Ir==       * r: the internal resistance of the battery       * I: current through the battery     * Internal resistance is measured by hooking a battery up to a resistor and plotting the terminal voltage of the battery as a function of the current through the battery       * The slope will be equal to -r
  • Switches   * Open switch: that part (loop) of the circuit can be considered gone (dead)
  • Capacitors   * __Capacitors__: two parallel metal plates separated by either air or dielectric material   * Capacitance: how much charge a capacitor can hold for each volt of potential difference     * ==C = kεA/d==       * C: capacitance       * k: dielectric constant       * ε: vacuum permittivity constant       * A: area of one of the plates (both plates have the same area)       * d: distance between plates   * ==ΔV = Q/C==     * ΔV: Voltage     * Q: charge     * C: capacitance (Farads)   * ==U = 1/2 QΔV = 1/2 C(ΔV )^2==     * U: energy stored in a capacitor     * Q: charge     * ΔV: potential difference     * C: capacitance   * ==ΔV/Δr = E==     * E: electric field     * ΔV: potential difference     * Δr: distance between plates
  • Parallel vs. Series Capacitors   * Parallel Capacitors     * ==C = ⅀Ci==       * C: total capacitance for capacitors in parallel       * Ci: capacitance of capacitors in parallel       * This is the same formula from resistors in series - capacitors are basically resistors in reverse   * Series Capacitors     * ==1/C = ⅀1/Ci==       * C: total capacitance for capacitors in series       * Ci: capacitance of capacitors in series

RC Circuits

  • __RC Circuit__: a circuit containing resistor(s) and capacitor(s)
  • You’ll only be asked about RC Circuits in certain states   * When you first connect a capacitor to a circuit:     * No charge has built up so treat the capacitor like a wire with no potential difference   * After a long time:     * The capacitor has charged up to its max so no current will flow through it     * Treat the capacitor like an open switch     * The potential difference across the capacitor equals the voltage of the devices parallel to the capacitor

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