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