Question

What is the value of ‘r’ in the following network if the equivalent resistance across AB is 1Ω?

Answer 1

Explanation:

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Answer 2

Answer:

The value of r is 6Ω

Explanation:

From the above question,

They have given :

R = equivalent resistance between the points A and B

If we imagine to stretch the points A and B apart and redraw it, we see that the circuit is a parallel combination of four similar resistors having resistance r each.

We also know that the following relation will be used to calculate the equivalent resistance between these two points.

R1 = 3Ω

R2 = 4Ω

R3 = 2Ω

AB = (R1 * R2) / (R1 + R2 + R3)

            AB = (3Ω * 4Ω) / (3Ω + 4Ω + 2Ω)

            AB = 1Ω

            R1 = 3Ω

            R2 = 4Ω

            R3 = 2Ω

             r = (R1 * R2) / (R1 + R2)

            r = (3Ω * 4Ω) / (3Ω + 4Ω)

            r = 6Ω

Hence, the equivalent resistance between the points A and B is $\frac{r}{4}$

The value of r is 6Ω

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