Branch current completion using KCL: A total of 120 mA enters a three-branch parallel network. Two branch currents are 40 mA and 10 mA. What is the third branch current?

Introduction / Context:
Kirchhoff’s Current Law (KCL) enables quick determination of unknown branch currents when the total entering or leaving a node and other branch currents are known. This is a common troubleshooting step in parallel circuits.

Given Data / Assumptions:

• Total incoming current I_total = 120 mA.
• Known branch currents: 40 mA and 10 mA (leaving the node).
• Steady-state; no charge storage at the node.

Concept / Approach:

By KCL, the sum of branch currents leaving the node must equal the current entering. Therefore, the third branch current equals the difference between total incoming current and the sum of the known branch currents.

Step-by-Step Solution:

Verification / Alternative check:

Check: 40 + 10 + 70 = 120 mA, which matches the total entering current. KCL satisfied.

Why Other Options Are Wrong:

50 mA confuses sum with difference. 120 mA ignores existing branches. 40 mA duplicates a known branch, not the computed one.

Common Pitfalls:

Sign errors (entering vs. leaving), and forgetting to subtract all known branch currents.

Final Answer:

70 mA