Wired Prism
Electricity and Magnetism
Level
3
Nine wires each of resistance 1 ohm are connected to make a prism. Find the equivalent resistance between A & B.
The answer is 0.6.
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1 solution
If we connect a voltage supply across A and B then by symmetry the potential at D and E is the same and the potential at C and F is the same, so the resistors DE and CF can be ignored. Then we have three branches of resistors in parallel. Firstly the two branches of 3 Ω in parallel gives 1 . 5 Ω then finally calculating with the AB resistor gives 1 + 1 . 5 1 × 1 . 5 = 0 . 6 Ω