What is the total current in the circuit after the series-parallel reduction for the 18 V source scenario?

What is the total current in the circuit after the series-parallel reduction for the 18 V source scenario?

• A. 0.5 A
• B. 0.75 A
• C. 0.25 A
• D. 1.034 A

Answer: (D)

The key idea is that the total current from the source depends on the voltage and the equivalent resistance seen by that source after you reduce all series and parallel paths into a single resistor. After the reduction, the circuit behaves like an 18 V source feeding a single resistance of about 17.4 Ω. Using Ohm’s law, the total current is I = V / R = 18 V / 17.4 Ω ≈ 1.034 A. This matches the given answer. If the current were 0.5 A, 0.75 A, or 0.25 A, that would imply equivalent resistances of 36 Ω, 24 Ω, or 72 Ω respectively, which would not correspond to the properly reduced circuit for the 18 V source.

The key idea is that the total current from the source depends on the voltage and the equivalent resistance seen by that source after you reduce all series and parallel paths into a single resistor. After the reduction, the circuit behaves like an 18 V source feeding a single resistance of about 17.4 Ω. Using Ohm’s law, the total current is I = V / R = 18 V / 17.4 Ω ≈ 1.034 A. This matches the given answer. If the current were 0.5 A, 0.75 A, or 0.25 A, that would imply equivalent resistances of 36 Ω, 24 Ω, or 72 Ω respectively, which would not correspond to the properly reduced circuit for the 18 V source.