kirchhoff's current law

Question

At a junction in a circuit, currents of 3 A, 2 A, and 4 A enter the junction. If one current of 5 A leaves the junction, what is the magnitude of the other outgoing current?

RankGuru · Accepted Answer

1. **Kirchhoff's First Law (Junction Rule)**: Sum of all currents entering a junction must equal the sum of all currents leaving that junction.
   - Based on the **Conservation of Charge**.
2. **Identify Entering Currents**:
   - $I_{in} = 3 	ext{ A} + 2 	ext{ A} + 4 	ext{ A} = 9 	ext{ A}$.
3. **Identify Leaving Currents**:
   - $I_{out} = 5 	ext{ A} + I_{unknown}$.
4. **Equate and Solve**:
   - $9 	ext{ A} = 5 	ext{ A} + I_{unknown}$
   - $I_{unknown} = 4 	ext{ A}$.
5. **Result**: The second outgoing current is 4 A.

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