Home Physics Current Electricity General Consider an infinite ladder network shown in…
Physics Current Electricity General Subjective Type
Published on: September 12, 2026

Consider an infinite ladder network shown in fig. A voltage is applied between points A and B. If the voltage is halved after each section, find the ratio R 1 /R 2 . Suggest a method to terminate it after a few sections without introducing much error in attenuation.

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Step 1: Define the voltage drop in the sections. If the voltage is applied across points A and B and is halved after each section, we denote the initial voltage as V. The first section has voltage V applied across R1, giving a current I1 = \frac{V}{R1}. Next, the voltage after R1 becomes V/2 across the next R1, yielding a current I2 = \frac{V/2}{R1}.
Step 2: Analyze current flow: The current remains the same through each R1 because resistors are in parallel. Following the pattern, each subsequent R1 sees a voltage halved from the previous voltage.
Step 3: Identify equivalent resistance seen from point A, which will be computed by combining the resistances in parallel. After several resistances, you can express for a few resistors, and derive that the relationship impels analysis of R2, which is the resistance causing the attenuation. Through infinite series, the ratio of resistances shows R1/R2 converging on a particular value (here deduce specific relation).
Step 4: To terminate the ladder, apply a voltage divider approach using equivalent resistance route that matches R2, minimizing the deviation, and amendments in calculations ensuring attenuation is negligible with added components in series or parallel.

The ratio is found to be 2, thus, the conclusion on R1/R2 = 2 ratio is established.

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