Diagnosing a parallel network from measured total current: Three-branch circuit with branch currents R1 = 12 mA, R2 = 15 mA, R3 = 25 mA. If the measured total is only 27 mA, what conclusion can you draw?

Introduction / Context:
Troubleshooting often involves comparing expected totals from branch data with measured totals. In a parallel circuit, the total current equals the sum of all branch currents. A discrepancy can immediately suggest an open branch or other fault.

Given Data / Assumptions:

• Expected branch currents: 12 mA, 15 mA, 25 mA.
• Measured total current: 27 mA.
• Assume the given branch values represent the normal operating currents.

Concept / Approach:

Compute the expected total and compare to the measured value. If the measured value equals the total minus exactly one branch, that branch is likely open (carrying 0 mA).

Step-by-Step Solution:

Verification / Alternative check:

If R3 were open, the total would be 12 + 15 = 27 mA, which matches the measured value. This confirms the diagnosis.

Why Other Options Are Wrong:

R1 open would give 15 + 25 = 40 mA. R2 open would give 12 + 25 = 37 mA. 'Operating properly' contradicts the mismatch. 'Multiple branches are shorted' would raise, not reduce, current.

Common Pitfalls:

Arithmetic slips adding branch currents; overlooking that an open branch contributes zero current.

Final Answer:

R3 is open