Equivalent Resistance in Series-Parallel Circuits

Steps:

• Identify configurations: series adds resistances (Req = R1 + R2 + ...), parallel uses reciprocals (1/Req = 1/R1 + 1/R2 + ...).
• Circuit 1: single resistor, Req = R.
• Circuit 2: two parallel branches, each with two series resistors (2R per branch), so Req = (2R × 2R)/(2R + 2R) = R.
• Circuits 3 and 4: different combinations yield Req ≠ R (e.g., 3: three in parallel, Req = R/3; 4: two in series, Req = 2R); circuit 5: balanced series-parallel, Req = R.

Why A is correct:

• Circuits 1, 2, and 5 all equivalent to R by series-parallel formula, as parallel halves the effective series value to match single R.

Why the others are wrong:

• B: Circuit 3 has Req = R/3 (three identical in parallel), not R.
• C: Circuit 4 has Req = 2R (two identical in series), not R.
• D: Circuits 2, 3, 4 have mismatched Req values (R, R/3, 2R).

Final answer: A