A parallel circuit contains an 18 ohm and a 9 ohm resistor. What is the total resistance?

A parallel circuit contains an 18 ohm and a 9 ohm resistor. What is the total resistance?

• A. 6 ohms
• B. 9 ohms
• C. 12 ohms
• D. 27 ohms

Answer: (A)

In a parallel circuit, the total resistance is found by considering how the paths for current add up. The conductances (the reciprocals of resistance) add in parallel, so 1/R_total = 1/18 + 1/9. That gives 1/18 + 1/9 = 1/18 + 2/18 = 3/18 = 1/6, hence R_total = 6 ohms. You can also compute it directly with the parallel formula R_total = (R1*R2)/(R1+R2) = (18*9)/(18+9) = 162/27 = 6 ohms. This result is expected because in parallel the total resistance is always less than the smallest individual resistance, thanks to the multiple current paths.

In a parallel circuit, the total resistance is found by considering how the paths for current add up. The conductances (the reciprocals of resistance) add in parallel, so 1/R_total = 1/18 + 1/9. That gives 1/18 + 1/9 = 1/18 + 2/18 = 3/18 = 1/6, hence R_total = 6 ohms. You can also compute it directly with the parallel formula R_total = (R1R2)/(R1+R2) = (189)/(18+9) = 162/27 = 6 ohms. This result is expected because in parallel the total resistance is always less than the smallest individual resistance, thanks to the multiple current paths.