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?
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A12 mA
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B48 mA
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C0 A
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D3 mA
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E24 mA
Answer
Correct Answer: 12 mA
Explanation
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:
Before the open: each branch draws 12 mA at the source voltage.One branch open: that path carries 0 mA; other branch parameters unchanged.Thus, each remaining branch continues to draw 12 mA.Only the total current from the source decreases by 12 mA.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