Physics · Ch 2 — Current Electricity

Kirchhoff's First Rule (Current Rule or Junction Rule)

2.5.1

Kirchhoff's First Rule (Current Rule or Junction Rule)

Kirchhoff's first rule, the current rule (or junction rule), states that the algebraic sum of the currents at any junction of a circuit is zero. By convention, current entering a given junction is taken as positive, and current leaving that junction is taken as negative. This rule is nothing more than a direct statement of the law of conservation of electric charge: whatever charge enters a junction in a given time must also leave it in that same time, because charge can neither build up nor simply disappear at a junction point. Applying the rule to a junction A at which five currents $I_1$ through $I_5$ meet (Figure 2.23), with the sign convention above, gives …

Figure 2.23Kirchhoff's current rule at a junction

What this figure shows. A junction point A has five current-carrying wires meeting at it, labelled $I_1$ , $I_2$ , $I_3$ , $I_4$ , $I_5$ with arrows showing each one's individual direction (some pointing into A, others pointing away from A) -- the figure that Kirchhoff's current rule, $I_1+I_2-I_3-I_4-I_5=0$ , is applied to directly, treating every arrow pointing into the junction as positive and every arrow po …

Misc Example 2.20Applying the junction rule to find an unknown branch current

Worked out. At a junction P, currents of 0.2 A and 0.6 A flow in, while currents of 0.4 A, 0.5 A and 0.7 A flow out, along with an unknown current I; the value of I is required. Taking currents into P as positive and out of P as negative, Kirchhoff's current rule gives $0.2-0.4+0.6-0.5+0.7-I=0$ , i.e. $1.5-0.9-I=0$ , so $0.6-I=0$ , giving $I=0.6$ A. …

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