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An infinite ladder network is built from identical sections: each section has a 1 ohm resistor in series along the top rail followed by a 2 ohm resistor shunting across to the bottom rail. What is the equivalent resistance measured between the input terminals P and Q?

1. 2 ohm
2. 3 ohm
3. 4 ohm
4. infinite

Correct answer: 2 ohm

Solution

Setting R = 1 + 2R/(2+R) gives R² - R - 2 = 0, whose positive root is R = 2 ohm.

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