The total resistance in a circuit is measured as 12 ohms in a parallel network. Which fault is most likely?

• A. There is an open in R2
• B. There is a short in R1
• C. There is an open in R1
• D. There is a short in R3

Answer: (C)

In a parallel circuit, a fault that shorts a branch lowers the overall resistance, because that branch becomes a near-zero path for current. An open in a branch removes that path, so the total resistance increases because only the remaining branches conduct.

Measuring a relatively high value like 12 ohms suggests a fault that removes one path rather than creates a near-short. That points to an open in R1, which eliminates that branch while the other resistors stay connected in parallel, raising the total resistance to the observed level. A short in any resistor would drive the total resistance down toward zero, which isn’t what's seen. An open in another branch could also raise Rt, but the option identifying an open in R1 best matches the described scenario.