Question

Find the equivalent resistance between
the points a and b of the infinite ladder
shown in figure.
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Answer 1

Please refer to the image attached for your answer.

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Answer 2

Question :

• Find the equivalent resistance between the points a and b of the infinite ladder shown in figure.

To Find :

• Equivalent resistance between a and b

Solution :

let the equivalent resistance resistance between a and b be R. As as the ledder is infinite, R is also the equivalent resistance of the ladder to the right of the point c and d. Thus we can replace the path to the right of cd by a resistance R and redrew the circuit as shown in figure.

Check attachment

This gives

$\tt R = r + \frac{rR}{r + R} \\ \\\tt rR + {R}^{2} = {r}^{2} + 2rR \\ \\ \tt {R}^{2} - rR - {r}^{2} = 0 \\ \\ \tt R = \frac{r + \sqrt{ {r}^{2} + 4 {r}^{2} } }{2} \\ \\ \boxed{\tt \green{ R = \frac{1 + \sqrt{5} }{2} r}}$