Series-parallel resistance combinations

Steps:

• Network Y: Three resistors in parallel, equivalent resistance $R_{eq} = \frac{R}{3}$.
• Network Z: Two resistors in parallel ( $\frac{R}{2}$ ) in series with one resistor, $R_{eq} = \frac{R}{2} + R = 1.5R$.
• Network X: Three resistors in series, $R_{eq} = 3R$.
• Compare values: $\frac{R}{3} < 1.5R < 3R$, so order Y, Z, X.

Why C is correct:

• C follows the parallel combination formula $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$ for lowest resistance in Y and series formula for highest in X.

Why the others are wrong:

• A: Places series X (3R) before parallel Y (R/3), reversing actual order.
• B: Correctly starts with Y but swaps X (3R) before Z (1.5R).
• D: Starts with Z (1.5R) before Y (R/3), ignoring parallel's lower resistance.

Final answer: C