Question

an infinite sequence of resistance is shown in the figure. the resultant resistance between a and b when r1 is 1ohms and r2 is 2ohms. with sol.​

Answer 1

Answer:

Equivalent Resistance between A and B

= 2 ohm...

hope, it helped you.

Answer 2

The resultant resistance between $a$ and $b$ is $2ohms$

Explanation:

Given,

In figure $R_{1}=1 ohms$ and $R_{2}=2 ohms$

Let total resistance of infinite series be R. hence circuit can be drawn as shown.

Here,

$R_{eqv}  = 1 + (R || 2)$

⇒$R_{eqv} =1+\frac{2R}{R+2}$

⇒$R_{eqv} =\frac{R+2+2R}{R+2}$

⇒$R_{eqv} =\frac{2+3R}{R+2}$

But,

$R_{eqv}  =R=Total resistance of infinite series$

⇒$R=\frac{2+3R}{R+2}$

⇒$R^{2}+2R =2+3R$

⇒$R^{2}-R-2=0$

⇒$R^{2}+2R-R-2=0$

⇒$R=2ohms$

So, The resultant resistance between $a$ and $b$ is $2ohms$