Current is charge flow, not energy flow

Current is the rate at which net charge crosses a chosen section:

One ampere is one coulomb per second. Conventional current follows positive-charge motion; in metals electrons drift the opposite way. With carrier number density n, charge magnitude |q|, cross-sectional area A, and average drift-speed magnitude vd, counting carriers in the swept volume Avd dt gives I=n|q|Avd.

Charge is not consumed by a resistor. In steady state the same current enters and leaves it. Energy is transferred to the material, largely through interactions of carriers with the lattice. A battery supplies energy by chemical processes; it does not create the circuit's charge.

Ohm's law is a material model

For an ohmic component under roughly fixed physical conditions,

Here V means the voltage drop across the component, R resistance, and ρ resistivity. Doubling wire length doubles resistance; doubling area halves it. A microscopic linear-response description is vec(J)=σvec(E), with conductivity σ=1/ρ. Combining J=I/A and E≈ V/L yields the macroscopic equation.

Ohm's law is not a universal law of all circuit elements. Diodes are nonlinear; a filament's resistance changes strongly as it heats. Even a metal resistor only approximately maintains constant resistance as temperature varies. Nor is a working resistive conductor an electrostatic-equilibrium conductor: a sustained internal electric field is needed to drive its current.

Derive power from energy per charge

A charge increment dQ falling through voltage V transfers energy dE=V dQ. Dividing by time gives

The last two forms apply to an ohmic resistor. Under the passive sign convention, current entering a component's higher-potential terminal corresponds to positive absorbed power. A source delivering energy has negative absorbed power.

A smaller resistance dissipates more power if its voltage is held fixed, but less if its current is held fixed. There is no contradiction: the external constraint differs. Never infer a trend from one symbol while silently changing another.

A small resistance can be a large problem

Consider a hypothetical low-voltage starter circuit carrying 100 A through a total lead/contact resistance of 0.020 Ω. The drop is IR=2.0 V, while heating is I²R=200 W. In five seconds the leads dissipate 1000 J. This is not a specification for a particular vehicle; it illustrates why high-current connections matter even when their resistance looks tiny.

If that resistance doubled, one cannot automatically say actual heating would double: the circuit current would generally change too. A starter is a motor with speed-dependent back emf, not a fixed resistor. The simple example prescribes current to isolate the loss mechanism; starting and charging places it in a working system.

Takeaway: Current measures charge per time, voltage energy per charge, and their product energy per time. These quantities describe different parts of one conservation story.