Electronics/Circuit fundamentals

Why resistance changes current

After thiswhat you will be able to doWork out current, voltage, or resistance from V = IR, and decide from a voltage-current relationship whether one fixed resistance is allowed.

Questionwhat this lesson answersIf voltage is energy per charge and current is charge per time, what property of a component links them, and when is the simple rule V = IR allowed?

Not coveredwhat this lesson leaves outWe use the linear model for fixed-temperature ohmic resistors and calculate their current and voltage. We do not derive resistance from atomic collisions or model components whose resistance changes with voltage or temperature.

Connect a resistor across an ideal source. The source sets the voltage difference. The resistor does not decide that every possible current should flow; it responds to the difference by allowing some charge to move and opposing the rest. The simplest model describes the response with

Rearrange it and the familiar form appears:

The unit of resistance is the ohm:

Resistance is not a fourth kind of flow. It is a ratio that describes how much voltage is needed to produce a given current through a component. A large resistance needs more voltage per ampere; a small resistance permits more current for the same voltage.

One calculation, three readings

Suppose an ideal source provides ${\SI{9}{V}}$ across a ${\SI{1}{k\Omega}}$ resistor. The current is

The same result can be read three ways. The source supplies ${\SI{9}{J}}$ per coulomb. The resistor requires ${\SI{1000}{V}}$ per ampere in this model. Therefore a current of ${\SI{0.009}{A}}$ is the rate that makes the resistor’s voltage drop ${\SI{9}{V}}$. Each statement uses a different quantity, but they agree because they are linked by the ratio.

If the resistance doubles while the source stays at ${\SI{9}{V}}$, the current halves. If the voltage doubles while the resistor stays at the same temperature, the current doubles. Those are predictions of the linear model, not general definitions of every electrical component.

When Ohm’s law is a model

People often say “Ohm’s law” as if every component must obey it. A resistor is ohmic when its voltage-current relation stays proportional under the conditions we care about. Its graph is a straight line through the origin, and the slope is the resistance. But the word resistance can still be used more broadly for the ratio ${V/I}$ at one operating point.

A filament lamp is a useful counterexample. Increase its current and the filament gets hotter. The hotter metal resists charge more strongly, so the next increase in voltage does not produce a proportional increase in current. A diode has a different nonlinear response: changing the voltage can move it from almost no current to a large current over a comparatively small range. For these components, the ratio ${V/I}$ changes as the operating point changes, so one fixed ${R}$ is not a complete description.

The microscopic explanation is material-dependent. Mobile charge carriers collide with a lattice, impurities, and other carriers; geometry also matters because a longer path and a smaller cross-section offer more opposition. Those details explain where resistance comes from, but the simple circuit calculation only needs the measured relationship.

Resistance belongs to a path

Voltage is measured between two points. Current is measured through a section. Resistance belongs to the relationship between those two ideas for one component or path. Saying “this battery has ${\SI{9}{V}}$” names a source difference. Saying “this resistor is ${\SI{1}{k\Omega}}$” describes what current that path produces for a given drop. Neither statement alone tells us the whole circuit until we know how the paths connect.

In a circuit with several resistors, some voltage drops occur one after another and some branches share the same two endpoints. The lesson on series and parallel circuits turns those connection patterns into rules for combining resistances.