Equivalent resistance determines battery current via Ohm's law

Steps:

• Calculate required equivalent resistance: R_eq = V / I = 6 V / 0.67 A = 9 Ω.
• Two 6 Ω resistors in parallel give 3 Ω; add third in series for 3 Ω + 6 Ω = 9 Ω.
• Total current through battery is V / R_eq = 6 V / 9 Ω = 0.67 A.
• Verify other configurations yield different currents.

Why A is correct:

• Configuration A has two resistors in parallel (3 Ω) in series with one (6 Ω), yielding R_eq = 9 Ω and I = 0.67 A per Ohm's law.

Why the others are wrong:

• B (all in series): R_eq = 18 Ω, I = 0.33 A.
• C (all in parallel): R_eq = 2 Ω, I = 3 A.
• D (two in series parallel with one): R_eq = 4 Ω, I = 1.5 A.

Final answer: A