Chapter revision
Revision summary
Key ideas, equations and common mistakes. Open any topic below for the full explanation.
Identify the charge-flow section, voltage endpoints and energy boundary before choosing an equation.
Charge, drift and energy transfer
I = nAvq (magnitude form)
V = W/Q
P = VI = I2R = V2/R
W = Pt (constant power)
- Current: Q/t is a mean over the interval, and is also the steady current when the flow rate is constant.
- Drift: n is carrier number density, A is cross-sectional area and v is mean drift speed. In the magnitude equation, q is positive carrier-charge magnitude; electron charge itself is -e. The count follows from volume AvΔt.
- Direction: electron drift is opposite conventional current. Charge is not used up in a resistor, and slow drift does not require a slow response of the whole circuit.
- Voltage: name both endpoints and a reference for potential levels. Adding the same constant to both levels leaves their difference unchanged.
- E.m.f.: source energy supplied per charge can exceed the external terminal transfer per charge during discharge. Account for the internal part separately.
- Power: use voltage and current of the same component. The resistor forms use V = IR; state whether current, voltage or resistance is fixed in a comparison.
For changing power, energy is the power-time area. Use 1 kWh = 3.6 × 106 J; kWh is energy and kW is power.
Measurement conditions
Put the ammeter in the component's path and the voltmeter across its terminals, with appropriate ranges, resolution and loading assumptions. Measured VI is electrical input; useful mechanical output requires a separate measurement.
Useful lifting work = mg(hfinish - hstart)
Efficiency = useful output / input
Use matched events and a steady motor/gear state with equal endpoint load speeds. For varying V and I, sum the time area of matched products ViIi, rather than multiplying separate means. Keep actual readings, model values and derived results distinguishable; investigate an impossible efficiency without altering the observations.
Return to the meter and measured-lift methods for the full procedure and error reasoning.
| Quantity | Symbol | Unit / meaning |
|---|---|---|
| Current | I | A = C/s |
| Transferred charge | Q | C = A s |
| Carrier charge | q | C; magnitude in I = nAvq |
| Elementary-charge magnitude | e | C; electron charge -e |
| Carrier number density | n | m-3; not moles |
| Cross-sectional area | A | m2 |
| Drift speed | v | m/s |
| Time interval | t or Δt | s |
| Potential level / difference | V | V = J/C; state reference / endpoints |
| Source e.m.f. | ε or E | V; source energy per charge |
| Resistance | R | Ω = V/A |
| Work / transferred energy | W or E | J; also kWh |
| Power | P | W = J/s |
| Raised mass / vertical rise | m, Δh | kg; m |
| Gravitational field strength | g | N/kg |
The symbol A can mean area while the unit A means ampere. W can mean work while the unit W means watt. E needs its local definition: it may denote e.m.f. in volts or energy in joules.
Return to charge flow and drift