Charge, voltage, current, resistance and electrical power

Ask which quantity crosses a boundary

Electric charge is measured in coulombs, C. Current is the rate at which net charge crosses a chosen surface: a constant current I transfers charge Q=It in time t. One ampere is one coulomb per second. Conventional current is referenced in the direction positive charge would move; electrons in a metal drift in the opposite direction. A current arrow defines a positive reference, not an observation of individual electrons.

Voltage is a difference between two electrical potentials. One volt corresponds to one joule per coulomb. Label both terminals or state a reference: Vab means potential at a relative to b. A node described as 6 V has meaning only relative to the chosen zero. That zero need not be the physical earth.

Use resistance with a stated model

A linear resistor obeys v=Ri under its declared conditions. Resistance R has units of ohms, Ω; one ohm is one volt per ampere. Real material response can change with temperature or operating state. A lamp, diode or motor is not automatically a fixed resistor because a voltage and current can be measured at one instant.

The original loop uses an ideal 6 V source, an ideal 300 Ω resistor and zero-resistance connections. The model current is 6/300=0.020 A, or 20 mA. In a steady series loop the same current passes every element: charge is not gradually consumed along the resistor. Real wires and sources require additional models when their resistance, limits or stored energy matter.

Describe energy transfer as well as current

Instantaneous power is p=vi. To use the passive sign convention, define positive current as entering the terminal labelled positive voltage. Positive p then means the element absorbs electrical power; negative p means it supplies power. In our loop the resistor absorbs 0.12 W and the ideal source supplies 0.12 W. The signed element powers sum to zero.

For a linear resistor, substitution gives p=i²R=v²/R. These are consequences of the resistor model, not interchangeable descriptions of every device. Power is an energy-transfer rate, measured in watts or joules per second. Energy transferred at constant power is Pt. A small current over a long interval can transfer substantial charge and energy; neither quantity is specified by the current alone.

Reconcile a fifty-second interval

Keep the constructed 20 mA current constant for 50 s. Net charge crossing any loop section is 0.020×50=1.0 C. The resistor’s power is 6×0.020=0.12 W, so it receives 0.12×50=6 J of energy.

The same answer follows from charge times potential difference: 1.0 C×6 J/C=6 J. This is an energy account, not a statement that one coulomb remains trapped or is destroyed inside the resistor.

If resistance doubled while the ideal source remained 6 V, current would halve to 10 mA and power to 0.060 W. Keeping current fixed instead would be a different source condition and a different comparison.

Try the reasoning

1. What is wrong with saying that current falls along this series resistor because energy is used?

   Show the answer and reasoning

   Steady series current is the same through it. Energy transfer changes the potential account, while charge continues through the loop.

2. Can “6 V at a point” stand alone as a complete voltage statement?

   Show the answer and reasoning

   It needs a reference potential. Voltage is a difference between two points.

3. Why is v²/R unsuitable for calculating every device’s power?

   Show the answer and reasoning

   It assumes v=Ri for a linear resistor. The more general terminal power account uses voltage, current and consistent signs.

What to carry forward

Track charge in coulombs, current in coulombs per second, voltage in joules per coulomb and power in joules per second.