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.
V = I·R, so I = V/R and R = V/I. The push, the flow and the opposition; the most useful relationship in electronics.
P = V·I, and since V = IR also P = I²R or P = V²/R. Use whichever pair you already have.
Series: same current, resistances add, voltage divides. Parallel: same voltage, currents add, 1/R = Σ1/Rn, always below the smallest branch.
KCL: ΣI in = ΣI out at any junction (charge does not pile up). KVL: voltage changes around any closed loop sum to 0.
For a fixed resistance P = V²/R, so doubling the voltage gives four times the power: why small voltage changes on heating elements or motors have an outsized effect on power draw.
Pick a current direction for each branch, guess freely, and let the algebra correct you. A negative answer is not an error: it means that current flows the other way. Kirchhoff’s laws are linear, so a wrong guess gives a correct negative number rather than a wrong answer. The only rule is consistency: once the arrows are drawn, write every equation to match them.
One source and one loop: Ohm’s law. More than one source, or a branch shared between loops, and Ohm still governs each resistor but cannot by itself say how the current divides: write KCL and KVL and solve them together, as the two-loop solver does.
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. Parallel always lowers resistance (more paths for current), series always raises it: two equal resistors give half in parallel, double in series.
Pure resistance on DC. AC adds reactance and phase from capacitors and inductors, where you would work with impedance instead. No tolerance, no temperature dependence, no source resistance.
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.
Parallel always lowers it (you're giving current more paths). Series always raises it. Two equal resistors in parallel give half; in series, double.
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.
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.
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.
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.
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.
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.
Ohm’s law V = I × R; power P = V × I; Kirchhoff’s current law, that the currents into a node sum to zero; and Kirchhoff’s voltage law, that the voltages around a closed loop sum to zero. Series resistances add; parallel ones combine as the reciprocal of the sum of the reciprocals.
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.