Effect of an open branch: A five-branch parallel circuit carries 12 mA in each branch. If one branch opens, what is the current in each of the remaining four branches?

Introduction / Context:
Parallel circuits deliver the same voltage to each branch. If a single branch opens, the other branches continue to operate unchanged as long as the source maintains its voltage. This concept is vital in fault tolerance and load-sharing designs.

Given Data / Assumptions:

• Total branches initially: 5.
• Branch current initially: 12 mA per branch.
• One branch opens; the source voltage remains constant and other branch resistances do not change.

Concept / Approach:

Branch current I_branch = V_source / R_branch. If V_source and R_branch for the remaining branches are unchanged, their individual currents remain the same even if the number of active branches changes.

Step-by-Step Solution:

Verification / Alternative check:

Compute total current: initially 5 * 12 mA = 60 mA; after open, 4 * 12 mA = 48 mA. Per-branch current remains 12 mA, confirming the conclusion.

Why Other Options Are Wrong:

48 mA is the new total, not the per-branch current. 0 A or 3 mA contradict the parallel rule with a regulated source. 24 mA doubles the branch current without cause.

Common Pitfalls:

Confusing total current with branch current; assuming the source voltage changes markedly when one branch opens.

Final Answer:

12 mA