Question

A network of resistance is constructed with $R_1$ & $R_2$ as shown in figure. The potential of points 1,2,3.......N are $V_1,V_2......V_N$ respectively, each having potential k times smaller than previous one, then ratio $\frac{R_1}{R_2}$ is

• A. $k^2-\frac{1}{k}$
• B. $(k-1)$
• C. $\frac{(k-1{)}^2}{k}$
• D. $k-\frac{1}{k^2}$

Answer 1

The correct option is C $\frac{(k-1{)}^2}{k}$

$V_0=i_0{R}_1+\frac{V_0}{k}$ & $\frac{V_0}{k}=i_1{R}_2$

$\frac{V_0}{k}=(i_0-i_1)R_1+\frac{V_0}{k^2}$

Using $i_0$ & $i_1$ is $\frac{V_0}{k}=\frac{V_0}{k^2}-\frac{V_0}{k}\frac{R_1}{R_2}+V_0-\frac{V_0}{k}$

On solving $\frac{R_1}{R_2}=\frac{(k-1{)}^2}{k}$