Two simple bookkeeping rules govern every circuit. One says charge cannot pile up at a junction; the other says energy is conserved around any loop. Together they let you solve circuits of any complexity.
Kirchhoff first law states that the total current into a junction equals the total current out, a statement of conservation of charge. Kirchhoff second law states that around any closed loop the sum of the e.m.f.s equals the sum of the p.d.s, a statement of conservation of energy. From these, resistors in series add (R = R₁ + R₂ + ...), while in parallel the reciprocals add (1/R = 1/R₁ + 1/R₂ + ...).
Switch resistors between series and parallel and watch the currents split and recombine while the totals obey both Kirchhoff laws and the combination rules.
Each law leads to one resistor rule.
| Rule | Statement | Origin |
|---|---|---|
| first law | ΣI in = ΣI out | conservation of charge |
| second law | ΣE = ΣIR around a loop | conservation of energy |
| series | R = R₁ + R₂ + ... | resistances add |
| parallel | 1/R = 1/R₁ + 1/R₂ + ... | reciprocals add |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
Kirchhoff first law is a statement of the conservation of:
Kirchhoff second law is a statement of the conservation of:
Two resistors of 3.0 Ω and 6.0 Ω are connected in series. Their combined resistance is:
The same 3.0 Ω and 6.0 Ω resistors connected in parallel give:
Kirchhoff laws tell you how current and voltage divide.
Add resistances directly only in series; in parallel you must add the reciprocals, and the result is always less than the smallest branch. In a parallel pair the voltage is shared (the same across each), while in series the current is shared (the same through each). When applying the second law, track the signs of e.m.f.s and p.d.s consistently around the loop.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
At a junction, currents of 3.0 A and 2.0 A flow in, and one current flows out. The current out is:
Three 6.0 Ω resistors are connected in parallel. Their combined resistance is:
A 12 V supply is connected across a 4.0 Ω and 8.0 Ω resistor in series. The p.d. across the 8.0 Ω resistor is:
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