An infinite ladder network is made of identical sections, each with a resistor in series and a resistor connected across the line after it. What is the equivalent resistance between the input terminals?
Answer and explanation
Correct answer: A. 4.61 Ω
- Step 1: For an infinite periodic ladder network, the equivalent resistance looking into the terminals remains unchanged if an additional section is added at the input: .
- Step 2: Substitute and : .
- Step 3: Multiply through by : .
- Step 4: Solve using the quadratic formula: . Taking the positive physical root yields .
Answer
4.61 Ω.
Why not the others: truncates the ladder after only a single section ().
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