Textbook Question
How much current flows through the bottom wire in FIGURE P28.66, and in which direction?
27. Resistors & DC Circuits
Kirchhoff's Junction Rule
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Five wires intersect at a point. Wires A, B, and C carry currents into the point, out of the point, and into the point, respectively. What can you say about the remaining two wires, D and E?
A
Both must be carrying current out from the point.
B
Both wires must be carrying current into the point.
C
One of the wires must be carrying current into the point, and one wire must be carrying current out of the point.
D
Each wire must be carrying of current.
E
At least one of the two wires must be carrying current out from the point.
Verified step by step guidance1
Understand the principle of conservation of charge, which states that the total current entering a junction must equal the total current leaving the junction.
Calculate the total current entering the junction. Wires A and C carry currents into the point, so add their currents: 3.0 A + 4.5 A = 7.5 A.
Calculate the total current leaving the junction. Wire B carries 1.0 A out of the point.
Apply the conservation of charge principle: the total current entering (7.5 A) must equal the total current leaving. Therefore, the sum of currents from wires D and E must be 6.5 A out of the point to balance the equation.
Conclude that at least one of the wires D or E must be carrying current out from the point to satisfy the conservation of charge.
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