Read Infinite Resistor Ladders by Self-Similarity
An infinite ladder is solvable because removing its first repeating block leaves a network identical to the original. Give the full equivalent resistance a name and use that repeat structure.
Electricity questions depend on identifying charge, a conducting path and the condition that controls current or magnetic effect.
Separate charge, current and the path between them
Charge is a property · current needs a conducting path
Charge is a property; current needs a conducting path. Decide first whether the question concerns charging, resistance, current or earthing.
Define the unknown once
Let R_eq be the resistance seen at the input. After the first series or parallel block, replace the entire remaining ladder by the same R_eq.
Translate the first cell
Write the exact series-parallel expression for only the first repeat cell. This creates one algebraic equation, usually quadratic.
Choose the physical root
Equivalent resistance must be positive and consistent with the smallest obvious resistance in the network.
OlympIQ exam lens
- ✓Locate the repeating cut.
- ✓Replace only the remaining tail by R_eq.
- ✓Reject negative or impossible roots.
Do not replace the whole diagram with R_eq before preserving the first cell; self-similarity starts after that cell.
Ready to try the pattern?
100% coverage across the linked question.
Practise the linked question