Consider an infinte ladder or network as shown in the adjacent figure. A voltage is applied between points A and B. If the voltage is halved after each section, find the ratio of $R_{1} / R_{2}$ .

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Solution

The correct option is B 1/2
Let the voltage between AB is V.
$I = I_{1} + I_{2}$
$\frac{v - v / 2}{R_{1}} = \frac{v / 2 - 0}{R_{2}} + \frac{v / 2 - v / 4}{R_{1}}$
$\frac{v / 2}{R_{1}} = \frac{v / 2}{R_{2}} + \frac{v / 4}{R_{1}}$
$\frac{1}{2 R_{1}} = \frac{1}{2 R_{2}} + \frac{1}{4 R_{1}}$
$\frac{1}{2 R_{1}} - \frac{1}{4 R_{1}} = \frac{1}{2 R_{2}}$
$\frac{2 - 1}{4 R_{1}} = \frac{1}{2 R_{2}}$
$4 R_{1} = 2 R_{2}$
$\frac{R_{1}}{R_{2}} = \frac{1}{2}$
Hence option A is correct.

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Consider an infinte ladder or network as shown in the adjacent figure. A voltage is applied between points A and B. If the voltage is halved after each section, find the ratio of R1/R2.

The correct option is B 1/2Let the voltage between AB is V.I=I1+I2v−v/2R1=v/2−0R2+v/2−v/4R1v/2R1=v/2R2+v/4R112R1=12R2+14R112R1−14R1=12R22−14R1=12R24R1=2R2R1R2=12Hence option A is correct.

Consider an infinte ladder or network as shown in the adjacent figure. A voltage is applied between points A and B. If the voltage is halved after each section, find the ratio of $R_{1} / R_{2}$ .