Consider the infinite resistance connection shown below each of resistor having resistance r If R be the equivalent resistance, then it can expressed in terms of r as.

Question

Consider the infinite resistance connection shown below each of resistor having resistance r If R be the equivalent resistance, then it can expressed in terms of r as. (A)  ((1+√5)/2)r  (B)  ((1-√5)/2)r  (C)  ((√3+1)/2√3)r  (D)  ((√7+1)/√3)r

Tardigrade Admin · Accepted Answer

Redrawing the resistance connection The equivalent resistance R=r+(rR/r+R)⇒ R2-rR-r2=0 ⇒ R=(r+√r2+4r2/2)=((1+√5)/2)r

Q. Consider the infinite resistance connection shown below each of resistor having resistance $r$
If R be the equivalent resistance, then it can expressed in terms of r as.

$\frac{( 1 + 5 )}{2} r$

$\frac{( 1 - 5 )}{2} r$

$\frac{( 3 + 1 )}{2 3} r$

$\frac{( 7 + 1 )}{3} r$

Redrawing the resistance connection
The equivalent resistance $R = r + \frac{r R}{r + R} \Rightarrow R^{2} - r R - r^{2} = 0$ $\Rightarrow$ $R = \frac{r + r ^{2} + 4 r ^{2}}{2} = \frac{( 1 + 5 )}{2} r$

Q. Consider the infinite resistance connection shown below each of resistor having resistance r If R be the equivalent resistance, then it can expressed in terms of r as.

2(1+5​)​r

2(1−5​)​r

23​(3​+1)​r

3​(7​+1)​r