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For the resistor network shown, find the equivalent resistance measured between terminals A and B.

1. 65 ohm
2. 20 ohm
3. 5 ohm
4. 2 ohm

Correct answer: 5 ohm

Solution

Such ladder/bridge networks are solved by successive series-parallel reduction. Resistors sharing a node with no other branch are in series (add directly); resistors sharing both end-nodes are in parallel (reciprocals add). If the bridge is balanced, the middle resistor carries no current and can be removed. Carrying out the reduction for this standard network collapses it to a single equivalent value of 5 ohm between A and B, which is much smaller than the largest individual resistor because the parallel paths dominate.

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