Power in series circuit from current

Steps:

• Power in fixed resistor: P = I²R, so 4 = I² × 20, I² = 0.2, I = √0.2 A.
• Total resistance R_total = R_var + 20 Ω.
• Current I = e.m.f. / R_total, so √0.2 = 16 / (R_var + 20).
• Solve: R_var + 20 = 16 / √0.2 = 16√5 ≈ 35.78, R_var ≈ 15.78 Ω ≈ 16 Ω.

Why A is correct:

• Matches calculation using P = I²R and Ohm's law, where I is uniform in series.

Why the others are wrong:

• B: Yields I ≈ 0.32 A, P ≈ 2.05 W (too low).
• C: Yields I ≈ 0.30 A, P ≈ 1.8 W (too low).
• D: Yields I ≈ 0.23 A, P ≈ 1.06 W (too low).

Final answer: A