Equivalent resistance of series-parallel circuit Steps: - Total resistance of circuit: R_total = emf / current = 6 V / 0.12 A = 50 Ω. - Circuit has 30 Ω in series with parallel combination of 60 Ω and R; parallel resistance R_p = (60 × R) / (60 + R). - Total resistance equation: 30 + R_p = 50, so R_p = 20 Ω. - Solve (60 × R) / (60 + R) = 20 → 60R = 20(60 + R) → 60R = 1200 + 20R → 40R = 1200 → R = 30 Ω. Why B is correct: - R = 30 Ω gives R_p = 20 Ω, so total resistance = 50 Ω, matching V = IR with given emf and current. Why the others are wrong: - A: 12 Ω gives R_p ≈ 8.6 Ω, total ≈ 38.6 Ω (current would be >0.12 A). - C: 60 Ω gives R_p = 30 Ω, total = 60 Ω (current = 0.1 A). - D: 80 Ω gives R_p ≈ 34.3 Ω, total ≈ 64.3 Ω (current …