State Kirchhoff's rules. Use them to find the current in each branch of a two-loop circuit containing two cells.

1. 1 · State the junction rule. At any junction, total current in = total current out (conservation of charge).
2. 2 · State the loop rule. Round any closed loop, the algebraic sum of changes in potential is zero (conservation of energy).
3. 3 · Draw and mark. [Circuit with junctions lettered, every emf and resistor labelled, currents I₁, I₂ and I₁ + I₂ marked, a curved arrow in each loop]
4. 4 · Write the loop equations. One per loop, with −IR along the current and +ε from − to +.
5. 5 · Solve. Solve the two equations for I₁ and I₂; get the third current from the junction rule.
6. 6 · Interpret the signs. A negative current flows opposite to the arrow drawn; that cell may be getting charged.
7. 7 · Check and box. The PD across a shared resistor must come out the same from both branches. Box each current with its unit.

Scoring tip: Write I₁ + I₂ in the shared branch at the start. It saves one unknown and one equation.