Constant Voltage Across Lamp Ensures Unchanged Power

Steps:

• Identify power dissipated in lamp: P = V² / R_lamp, where R_lamp is fixed.
• Note battery has constant ε and negligible internal resistance, so terminal voltage equals ε.
• For P to remain constant as variable resistor (R_var) adjusts, voltage V across lamp must stay at ε.
• This occurs only if R_var is in parallel with lamp, keeping lamp voltage fixed at ε regardless of R_var value.

Why A is correct:

• In circuit A, R_var parallels the lamp, so lamp voltage remains ε (by voltage divider rule for parallel branches), yielding constant P = ε² / R_lamp.

Why the others are wrong:

• B: R_var in series with lamp; total resistance changes, so current I = ε / (R_lamp + R_var) varies, altering P = I² R_lamp.
• C: R_var in series with parallel lamp-battery setup; effective load changes, varying lamp current and power.
• D: R_var shunts battery-lamp series; adjusts current split, changing lamp voltage and power.

Final answer: A