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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

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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