Topic: Network Theory
The approximate equivalent resistance between terminals A and B for the following infinite ladder network comprising of 1 $\Omega$ and 2 $\Omega$ resistors is
- A. 1 $\Omega$
- B. 2 $\Omega$
- C. 4 $\Omega$
- D. 0.5 $\Omega$
Answer: B. 2 $\Omega$
Explanation: Let the equivalent resistance be $R_{in}$. Since the ladder is infinite, adding one more stage will not change the equivalent resistance. So, $R_{in}=1+\frac{2R_{in}}{2+R_{in}} = \frac{2+R_{in}+2R_{in}}{2+R_{in}} = \frac{3R_{in}+2}{2+R_{in}}$. $R_{in}^{2}+2R_{in}=3R_{in}+2 \Rightarrow R_{in}^{2}-R_{in}-2=0$. Therefore, $(R_{in}-2)(R_{in}+1)=0 \Rightarrow R_{in}=2~\Omega$.