Connect current, voltage and resistance

From a stationary charge to a steady flow

A circuit can transfer energy continuously while its charge distribution remains approximately steady. Current is the rate at which net charge passes a cross-section: I = ΔQ/Δt, where I is current in amperes (A), ΔQ is charge in coulombs (C), and Δt is elapsed time in seconds (s). One ampere is one coulomb per second; 1 mA = 0.001 A. Conventional current follows the direction positive charge would move. In a metal, electron drift is opposite that direction.

Voltage is different: it measures energy change per charge between two points. Resistance relates a component’s voltage drop to its current. For an ohmic resistor under fixed conditions, V = IR, where resistance R is measured in ohms (Ω). This proportional relationship is a model for suitable components, not a promise that every device has constant resistance.

Try both circuits at the same voltage

The browser supplies two separate sources and the same resistor values in two connections. At the default 6 V, the series source delivers 20 mA, while the parallel source delivers 90 mA. The different currents do not contradict the common voltage: the connections present different equivalent resistances, 300 Ω and 66.667 Ω respectively.

Before changing voltage to 12 V, write the expected currents. Capture both settings with R2 held at 200 Ω. The model gives 40 mA and 180 mA, twice the corresponding initial currents. The larger current is not faster motion of the drawn arrow; arrows indicate reference direction only.

At 20 mA held for 60 s, charge passing through the series source is (0.020 A)(60 s) = 1.2 C. At 90 mA it is 5.4 C. This counts transported charge, not charge created by the source or consumed by a resistor. The model has no particle-tracking animation and does not calculate electron drift speed.

Read the slope with its axes

The graph has current on the vertical axis and voltage on the horizontal axis. Its slope is I/V = 1/R equivalent, called conductance. A steeper line indicates smaller equivalent resistance. On a graph with voltage vertical and current horizontal, the slope would instead be resistance. Always identify axes and units before interpreting a slope.

At 0 V both model currents are zero, but the connected resistor networks still have their defined equivalent resistances. The ratio 0/0 cannot measure resistance from that one point; use nonzero readings or the slope. Zero source voltage is not the same circuit condition as a broken wire.

Transfer beyond the sliders

A steady 15 mA current passes a point for 40 s. How much charge passes? Separately, an ohmic component has 3 V across it and carries 15 mA. Infer its resistance and predict current at 4.5 V if its resistance stays constant.

OpenStax: electrical current explains charge flow and direction. Ohm’s law discusses the proportional model and its limits. The browser values above are original synthetic comparisons, not measurements.