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Q.
An infinite ladder network is arranged with resistances $R$ and $2\, R$ as shown. The effective resistance between terminals $A$ and $B$ is
Current Electricity
Solution:
Let equivalent resistance between $A$ and $B$ is $R'$, so given circuit can be reduced as follows
$R'=R+\frac{2 R \times R'}{\left(2 R+R'\right)}$
$\Rightarrow R^{'2}-R R'-2 R^{2}=0$
On solving the equation we get $R=2 R$.
