Electrical · electronics

Electrical Circuit

Ohm's law, Kirchhoff's current and voltage laws, and resistor networks. Standalone bands: Resistor Colour Code →
V = I·R · P = V·I
12 V · 3 A

Ohm's law

any two

The circuit

Suggested wire gauge
general-purpose reference, not an electrical code
All four quantities
Resistor networks

Series & parallel

add resistors, get both totals
In series (end to end)
Resistances add up. The total is always larger than the biggest one.
In parallel (side by side)
Reciprocals add. The total is always smaller than the smallest one.
Kirchhoff's laws

Two loops, two sources

solved, with the working shown

Ohm's law handles one resistor. The moment a circuit has more than one loop or more than one source, you need Kirchhoff's two laws: current is conserved at every junction, and voltage around any closed loop sums to zero. Below is the circuit those laws are always taught on — two supplies sharing a middle branch. Change any value and the currents are re-solved.

The working

Current law

Junction check

leave one blank to solve it
Field notes

The relationships worth memorising

How it works

Ohm's law in one place

Ohm's law ties together voltage (V, the push), current (I, the flow), and resistance (R, the opposition): V = I·R. Add power (P = V·I, in watts) and you have four quantities where knowing any two gives the other two. Pick your two knowns, type them in, and the rest fall out.

Worked example

A 12 V supply across a 4 Ω resistor drives 3 A (12 ÷ 4) and dissipates 36 W (12 × 3). Double the resistance to 8 Ω and the current halves to 1.5 A — and the power drops to 18 W.

Put two 4 Ω resistors in series and you get 8 Ω; put them in parallel and you get 2 Ω. That's how you hit a resistance you don't have a single part for.

Which power formula should I use?

Whichever fits what you know: P = V·I, or P = I²·R, or P = V²/R. They're all the same law rearranged. This tool computes all of them for you.

Series or parallel — which lowers resistance?

Parallel always lowers it (you're giving current more paths). Series always raises it. Two equal resistors in parallel give half; in series, double.

Does this handle AC?

No — this is DC and pure resistance. AC adds reactance and phase from capacitors and inductors, where you'd work with impedance instead of plain resistance.

What is Kirchhoff's current law (KCL)?

At any junction, the currents flowing in equal the currents flowing out: Σ Iin = Σ Iout. It is conservation of charge — charge cannot pile up at a point in a wire. Use the junction check above to solve for a missing branch current.

What is Kirchhoff's voltage law (KVL)?

Around any closed loop the voltage changes sum to 0 — rises across sources, drops across resistors (I·R each). You finish where you started, so you finish at the same potential.

When do I need Kirchhoff rather than Ohm's law?

As soon as there is more than one source, or a branch shared between two loops. Ohm's law still governs each resistor, but it cannot by itself tell you how the current divides — for that you write KCL and KVL and solve them together, which is what the two-loop solver above does.

Why is one of my currents negative?

Because the direction you assumed was the opposite of the real one. That is not a mistake — it is the sign convention working. Pick any direction you like, stay consistent, and let the algebra correct you: a negative answer means the same magnitude flowing the other way.

Why does power matter?

Power is heat. A resistor rated for ¼ W will burn out if you push 1 W through it, even if the resistance is "right." Always check the power against the component's rating.

Results are for reference only. Ideal DC resistive model — real components have tolerance, temperature drift, and ratings. Mind live circuits and power limits.
Version history · 1 release
  1. v0.822026-07-28Kirchhoff's laws added to Electrical Circuit; knowledge doc caught up 43 versions and its counts made self-stamping

Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.