Revision summary

Identify the charge-flow section, voltage endpoints and energy boundary before choosing an equation.

Charge, drift and energy transfer

• 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.

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 V_iI_i, 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.

Sinusoidal quantities and equivalent heating

The half-peak mean-power and divide-by-√2 results require a sinusoid and the stated constant resistive load. The general rms meaning is equivalent d.c. heating in the same resistor. Zero mean signed current can still give positive mean power.

For i = 4 sin(100πt) A through 6 Ω: T = 20 ms, f = 50 Hz, voltage peak 24 V, power peak 96 W and mean power 48 W. Current/voltage reverse together; power repeats every 10 ms. Energy over a full current cycle is 0.960 J.

Single-diode output

With diode anode A, cathode B and resistor B-to-C, positive V_A - V_C conducts and the negative half-cycle blocks. Output V_B - V_C is zero when blocked. The ideal positive pulses retain the input peak but repeat once per full input period; they are not steady current. Use the full waveform when finding rms, rather than reusing a sinusoidal peak rule.

Review the equal-area rms deduction or trace the two diode states.

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. Lowercase i and p denote instantaneous current and power. Lowercase v on the alternating-voltage graphs denotes instantaneous voltage, rather than the drift speed v used in the carrier model.