Equivalent resistance in series-parallel networks

Steps:

• Identify configurations: X has all resistors in parallel (lowest resistance), W has all in series (highest), Z and Y are mixed series-parallel.
• Calculate R_X: for n equal resistors in parallel, R_X = R/n (smallest equivalent).
• Calculate R_Z and R_Y: apply parallel rule first (1/R_eq = sum 1/R_i), then add series (R_total = sum R_eq), yielding R_Z < R_Y.
• Compare: R_X < R_Z < R_Y < R_W confirms increasing order.

Why D is correct:

• Option D orders networks by calculated equivalents: X (parallel, minimal) to Z (moderate mix) to Y (higher mix) to W (series, maximal), per parallel (reduces) and series (adds) formulas.

Why the others are wrong:

• A starts with W (highest, not lowest).
• B omits W and starts with X but skips Z's position.
• C includes W too early, misordering Y and W.

Final answer: D