In a series circuit with V=12V, R₁=10Ω, R₂=20Ω — what is the total current?

You can work it out this way: find R_eq first (series), then use I = V / R_eq.

Switch to parallel with the same values. How does total current change and why?

Parallel R_eq is less than either resistor — more current flows from the same voltage.

In parallel mode, if R₁=10Ω and R₂=30Ω, what fraction of total current flows through R₁?

Each branch current: I = V/R. Ratio of currents = R₂/R₁ (inverse of resistance).

Pro 🔒~30 min

DC Circuits — Ohm's Law

Series and parallel resistors with live current visualization

How it works

Ohm's Law states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. In series circuits, resistors share the same current but split the voltage; the equivalent resistance is the sum of individual resistances. In parallel circuits, resistors share the same voltage but split the current; the reciprocal of equivalent resistance equals the sum of reciprocals. Understanding these two configurations is fundamental to analyzing any real-world circuit.

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Step-by-step

Use the Series / Parallel toggle to switch circuit configurations.
Adjust voltage and resistors to observe how current (particle flow speed) and equivalent resistance change.
The glowing dots represent electrons — faster movement means higher current.
Blue particles flow through R₁, amber through R₂ in parallel mode.

Key formulas

$V = IR$ Ohm's Law
$R_{series} = R_1 + R_2 + R_3$ Series equivalent resistance
$\frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2}$ Parallel equivalent resistance
$P = IV = I^2R = \frac{V^2}{R}$ Power dissipated

Frequently asked questions

In a series circuit with V=12V, R₁=10Ω, R₂=20Ω — what is the total current?: You can work it out this way: find R_eq first (series), then use I = V / R_eq.
Switch to parallel with the same values. How does total current change and why?: Parallel R_eq is less than either resistor — more current flows from the same voltage.
In parallel mode, if R₁=10Ω and R₂=30Ω, what fraction of total current flows through R₁?: Each branch current: I = V/R. Ratio of currents = R₂/R₁ (inverse of resistance).