Parallel-series resistor network

Steps:

• Two resistors in series have equivalent resistance 2R; this branches in parallel with resistor X (R), giving total Req = (R × 2R)/(3R) = (2/3)R.
• Battery current I = 0.3 A = V / Req, so voltage V across parallel section = 0.3 A × (2/3)R = 0.2R.
• Current in X = V / R = 0.2R / R = 0.2 A.
• Total current splits: 0.2 A through X, 0.1 A through series branch.

Why C is correct:

• By Ohm's law, current in parallel resistor X is voltage across parallel combination divided by R, yielding 0.2 A.

Why the others are wrong:

• A: 0.1 A is current through each series resistor (V / 2R).
• B: 0.15 A assumes equal current split, ignoring series branch higher resistance.
• D: 0.3 A is total battery current, not branch current.

Final answer: C