Physics - Current Electricity Question with Solution | TestHub

A. For an infinite ladder where each section consists of a series resistor $R$ followed by a parallel combination of $R$ and the rest of the infinite ladder ($R_{eq}$), the equation is $R_{eq}=R+\frac{R{R}_{eq}}{R+R_{eq}}$. B. Solving the quadratic equation from A: $R_{eq}(R+R_{eq})=R(R+R_{eq})+R{R}_{eq}⟹R_{eq}^2-R{R}_{eq}-R^2=0$. The positive solution is $R_{eq}=R\frac{1+\sqrt{5}}{2}$.

C. For this type of infinite ladder, the equivalent resistance of a finite number of sections approaches the infinite ladder's resistance from below, so it is less than $R_{eq}$ for finite $N$. D. This is the fundamental definition of the equivalent resistance of an infinite ladder network.