Question

Determine the resultant resistance of the infinite circuit made of r resistance between A and B –

• A. 1.2 r
• B. 5 r
• C. 4.2 r
• D. 8 r

Answer 1

Answer: (A)

1.2 r

Answer 2

By symmetry equivalent circuit

Where R_eq in the resistance between A and B

$\frac{(R_{eq} + 2r) \times 2r}{R_{eq} + 4r}$= R_eq

2rR_eq + 4r² = $R_{eq}^{2}$+ 4r R_eq

$R_{eq}^{2}$ + 2rR_eq – 4r² = 0

R_eq = $\frac{- 2r \pm \sqrt{4r^{2} + 16r^{2}}}{2}$

= $\frac{- 2r \pm \sqrt{20r^{2}}}{2}$

= $\frac{- 2r + 4.5r}{2}$

= 1.23 r