Resolved Problems about Electrical Resistance

Problem 2.18 Source: Problem elaborated by the author of the site.

Calculate the value of R in the circuit shown in Figure 02-18.1, so that R_ab = R_x.

Solution of the Problem 2.18

To solve this problem, the equivalent circuit resistance must be found in the terminals a-b. And this value must be equal to R_x. So let's calculate the resistance along the path 1-2-3-4:

R₁₂₃₄ = R_x + 4 R

To find the resistance between the points 1-4, you must calculate the parallel between R₁₂₃₄ and 16 R. Then:

R₁₄ = 16 R (R_x + 4 R) / (R_x + 20 R)

And to find the resistance between the points a-b, add 4 R to R₁₄. And this result must be equal to R_x. After an algebraic arrangement, the following relation is reached:

64 R² + 16 R R_x + 80 R² + 4 R R_x = 20 R R_x + R_x²

Performing the calculation results in the following relation:

144 R² = R_x²

Therefore, the result sought is:

R = R_x / 12

Back to Top

Previous Problem

Next Problem