A DC voltage source is applied across the input of a finite resistor ladder network. The network has a common ground line and a top line with 4 nodes (including the input node). There are 3 resistors, each of resistance R , connected in series between adjacent nodes on the top line. A shunt resistor of 2R is connected from the input node to the ground line, and similarly, a 2R resistor is connected from each of the n

Step-by-step solution

Let the nodes on the top line be N₀ (input), N₁, N₂ , and N₃ (far-end). Starting from the far end, the equivalent resistance of the ladder to the right of N₂ is the series combination of R (between N₂ and N₃ ) and R (at N₃ to ground), which is 2R . At N₂ , this 2R branch is in parallel with the shunt resistor 2R , giving an equivalent resistance of R . This pattern repeats. The equivalent resistance looking into the ladder from N₁ (excluding its shunt) is 2R , and including its shunt is R . At the input node N₀ , t