In a circuit with three 12-ohm resistors in series (36 ohms) and in parallel (4 ohms), which statement is true?

In a circuit with three 12-ohm resistors in series (36 ohms) and in parallel (4 ohms), which statement is true?

• A. The series arrangement has higher total resistance than the parallel arrangement
• B. The parallel arrangement has higher total resistance than the series arrangement
• C. They have the same total resistance
• D. Only one arrangement conducts current

Answer: (A)

Resistance adds in series and decreases in parallel. When three 12-ohm resistors are in series, the total is 12 + 12 + 12 = 36 ohms. In parallel, the reciprocals add: 1/R = 1/12 + 1/12 + 1/12 = 3/12, so R = 4 ohms. Therefore, the series arrangement has the higher total resistance (36 ohms) compared to the parallel arrangement (4 ohms). With the same voltage, the parallel path would allow more current, since it presents a lower resistance. Also, both configurations would conduct current if a voltage source is connected, so the idea that only one arrangement conducts isn’t correct.

Resistance adds in series and decreases in parallel. When three 12-ohm resistors are in series, the total is 12 + 12 + 12 = 36 ohms. In parallel, the reciprocals add: 1/R = 1/12 + 1/12 + 1/12 = 3/12, so R = 4 ohms. Therefore, the series arrangement has the higher total resistance (36 ohms) compared to the parallel arrangement (4 ohms). With the same voltage, the parallel path would allow more current, since it presents a lower resistance. Also, both configurations would conduct current if a voltage source is connected, so the idea that only one arrangement conducts isn’t correct.