In the infinite grid, if the value of r=2(√5-1) Ω, find the equivalent resistance between the points a and c.

Question

In the infinite grid, if the value of r=2(√5-1) Ω, find the equivalent resistance between the points a and c. (A) 6(√5-1) Ω (B) 4(√5-1) Ω (C) 4 Ω (D) none of these

Tardigrade Admin · Accepted Answer

Due to symmetry, the line of resistors passing through b will be useless. re q=2 r+(2 r re q/2 r+re q) ⇒ re q=(1+√5) r =(√5+1) 2(√5-1)=4 Ω

Q. In the infinite grid, if the value of $r = 2 (5 - 1) Ω$ , find the equivalent resistance between the points $a$ and $c$ .

$6 (5 - 1) Ω$

$4 (5 - 1) Ω$

$4 Ω$

none of these

Due to symmetry, the line of resistors passing through $b$ will be useless.
$r_{e q} = 2 r + \frac{2 r r _{e q}}{2 r + r _{e q}}$
$\Rightarrow r_{e q} = (1 + 5) r$
$= (5 + 1) 2 (5 - 1) = 4 Ω$

Q. In the infinite grid, if the value of r=2(5​−1)Ω, find the equivalent resistance between the points a and c.

6(5​−1)Ω

4(5​−1)Ω

4Ω