Circuits put electric potential to work: a battery's emf drives current through resistors, bulbs and capacitors. You'll find equivalent resistance, apply Kirchhoff's loop and junction rules, read meters, and follow how an RC circuit changes with time. It is one of the two heaviest units on the exam.
- electric current
- The rate at which charge passes through a cross section of a conductor: I = dq/dt. Unit: ampere, 1 A = 1 C/s.
- Example: If 30 C of charge passes a point in a wire in 6.0 s, the current is I = 30/6.0 = 5.0 A.
- closed, open and short circuit
- Closed circuit: a complete loop, so charge can flow. Open circuit: a break, so no charge flows. Short circuit: charge flows with no change in potential.
- Example: Opening a switch in series with a bulb turns it off (open); laying a bare wire across the bulb's terminals also turns it off (short).
- resistance
- A measure of how strongly an object opposes the movement of charge through it. Unit: ohm (Ω), where 1 Ω = 1 V/A.
- Example: With the same potential difference across each, a 1000 Ω resistor passes one hundredth the current of a 10 Ω resistor.
- electric power
- The rate at which a circuit element transfers energy: P = IΔV. For a resistor, P = I²R = (ΔV)²/R; resistors convert electrical energy to thermal energy.
- Example: A 6.0 Ω resistor carrying 2.0 A uses P = (2.0)²(6.0) = 24 W, or 24 J each second.
- series connection
- Elements joined end to end in a single path: any charge passing through one must pass through all. Every element in series carries the same current.
- Example: A bulb, a resistor and an ammeter in one loop with a battery all carry the same current, whatever order they are in.
- Kirchhoff’s loop rule
- Around any closed loop, the potential differences across all the elements add to zero: ΣΔV = 0. It follows from conservation of energy.
- Example: 12 V battery with 4.0 Ω and 2.0 Ω in one loop: 12 − 4.0I − 2.0I = 0, so I = 2.0 A.
- capacitors in series
- For capacitors in series, 1/C_eq = 1/C₁ + 1/C₂ + …. Conservation of charge gives each the same charge, and C_eq is less than the smallest capacitance.
- Example: 4.0 μF and 12 μF in series: 1/C_eq = 1/4.0 + 1/12, so C_eq = 3.0 μF, less than either.
- drift velocity
- The slow average velocity of charge carriers along a conductor: I = nqv_dA, with n carriers per m³ of charge q. Zero current means zero average, though carriers still move.
- Example: n = 8.5 × 10²⁸ m⁻³, A = 1.0 mm², I = 1.36 A: v_d = I/(neA) = 1.0 × 10⁻⁴ m/s.
- circuit schematic
- A diagram of a circuit using standard symbols for batteries, bulbs, switches, capacitors, resistors, ammeters, voltmeters and inductors. A diagonal arrow through a symbol marks a variable element.
- Example: A resistor symbol with a diagonal arrow drawn through it is a variable resistor, one whose resistance can be adjusted.
- resistivity
- A property of a material, set by its atomic and molecular structure, that measures how strongly it opposes charge motion. Unit: Ω·m. A conductor's resistivity usually rises with temperature.
- Example: Copper's resistivity is about 1.7 × 10⁻⁸ Ω·m at room temperature, and a hot copper wire has a higher value.
- lightbulb brightness
- A bulb's brightness increases with the power it uses, so rank bulbs by P. Identical bulbs in series on a battery are each dimmer than one bulb alone on it.
- Example: Two identical bulbs in series share a battery's ΔV, so each uses a quarter of the power that one bulb alone would use.
- parallel connection
- Elements connected across the same two points, giving charge two or more paths. Each path has the same potential difference across it.
- Example: A 4.0 Ω and a 12 Ω resistor, each wired directly across a 6.0 V battery, both have 6.0 V across them.
