LC

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