Equivalent circuit analysis for power dissipation

Steps:

• Left circuit: single cell (ε) in series with single R; current I = ε/R; power in R is P = I²R = ε²/R.
• Right circuit: two cells in parallel (equivalent emf ε, negligible resistance) in series with two R (equivalent resistance 2R).
• Current in right circuit: I_right = ε / 2R.
• Total power in right: I_right² × 2R = (ε / 2R)² × 2R = ε² / (2R) = P/2.

Why B is correct:

• Total power equals supply power from equivalent battery: ε × I_right = ε × (ε / 2R) = ε² / (2R) = P/2, matching the formula for resistive dissipation.

Why the others are wrong:

• A: P/4 would require 4R equivalent, but right has 2R.
• C: P assumes same resistance as left, but right doubles it.
• D: 2P would require parallel resistors halving resistance, but right uses series.

Final answer: B