Mixed series–parallel network with a fault — four identical 10 kΩ resistors are connected in parallel to form a branch, and this parallel branch is in series with a 20 kΩ resistor and an ideal source. If one of the parallel branches develops a hard short (0 Ω path across the parallel group), what happens to the voltage across the remaining parallel resistors?

Introduction / Context:
Diagnosing faults in series–parallel networks requires recognizing how a single failure can change node voltages and element stresses. A short across a parallel group is a classic fault that collapses the node voltage feeding all other parallel elements, affecting both operation and safety margins.

Given Data / Assumptions:

• Four 10 kΩ resistors are in parallel as a single branch.
• This parallel branch is in series with a 20 kΩ resistor and a source.
• One branch in the parallel group fails as a near-ideal short (0 Ω) effectively across the entire parallel node pair.
• Wires and source are otherwise ideal.

Concept / Approach:
In any parallel network, all components share the same node-to-node voltage. If a hard short is placed across the parallel node pair, the node pair becomes equipotential (no difference), so the voltage across that entire group becomes approximately 0 V. Therefore, every remaining parallel resistor sees zero volts and, consequently, zero current. The series 20 kΩ now carries whatever current is determined by the source and the shorted path, not by the original parallel combination.

Step-by-Step Solution:

Verification / Alternative check:
Replace the entire parallel group with its equivalent. With a short across the output nodes of the group, the equivalent becomes 0 Ω. The series chain reduces to 20 kΩ in series with 0 Ω to ground, making the node feeding the group at ground potential relative to the group—hence 0 V across it.

Why Other Options Are Wrong:

Common Pitfalls:
Thinking only the shorted branch is affected; in reality, the short collapses the voltage for the entire parallel group. Also, overlooking power implications in the series element and the shorted path.

Final Answer:
Drops to zero