الأسبوع 3 · الفصل الأول (٣): قانونا كيرتشوف (حفظ الشحنة وحفظ الطاقة) وإرشادات اتجاهات التيار والإشارات، وثلاثة أمثلة محلولة لدوائر ذات أكثر من مسار مغلق · 3 دروس
1
Kirchhoff’s first law: currents at a junction
Physics Sec 3 Term 1, Chapter 1: pp. 18–23
GoalState the first law, use it at a junction with assumed directions, and read the sign of a result.
New words
junction (node) · a point where three or more wires meetKirchhoff’s first law · the currents flowing into a junction add up to the currents flowing out of itconservation of charge · charge is neither made nor destroyed, so it cannot pile up at a point
Explanation
Ohm’s law is enough for series and parallel circuits, but some circuits have several sources and several loops. For them the scientist Gustav Kirchhoff gave two laws. The first is about a junction, a point where three or more wires meet. Charge does not pile up at a point and is not made or lost there, so as much charge flows into a junction each second as flows out of it. In symbols, Σ I(in) = Σ I(out). You may also count currents into the junction as plus and currents out of it as minus, and then the sum is zero. If you do not know the direction of a current, assume one and go on. When the answer comes out negative, the real current flows the other way. You have used the law already: in a parallel circuit the branch currents add up to the total current.
Wire
Direction
Current (A)
a
into the junction
7
b
into the junction
3
c
out of the junction
4
d
out of the junction
?
Worked examples
Wire
Direction
Current (A)
a
into the junction
7
b
into the junction
3
c
out of the junction
4
d
out of the junction
?
Currents of 7 A and 3 A flow into a junction. A third wire takes 4 A out, and a fourth wire takes the rest out. Into the junction: 7 + 3 = 10 A. Out of it: 4 + I. So 10 = 4 + I, and I = 6 A out of the junction.
Five wires meet at a point. One carries 5 A in, one 2 A out and one 4 A out. For the fourth wire we assume a current I out of the junction: 5 = 2 + 4 + I, so I = −1 A. The minus sign says that the real current of 1 A flows into the junction.
A source feeds three parallel branches that carry 1.2 A, 0.8 A and 0.5 A away from the junction. The current from the source into the junction is 1.2 + 0.8 + 0.5 = 2.5 A.
Class activity
On paper, draw a junction with four wires: 6 A and 2.5 A flow in, 3 A flows out, and the fourth wire is unknown. Use the law to find it and say whether it flows in or out. Then draw the same junction as water pipes with litres per minute, and explain why the water cannot pile up at the joint.
Practice
1
Into a junction flows 9 A. One wire takes 4 A out. Find the current in the only other wire, which is also out of the junction.
9 = 4 + I, so I = 5 A out.
2
Currents of 3 A and 8 A flow into a junction. One wire carries 6 A out and a second wire carries I out. Find I.
3 + 8 = 6 + I, so I = 5 A out.
3
At a junction 2 A flows in, and 3 A and 4 A flow out. A fourth wire is assumed to carry a current I into the junction. Find I and say what the sign means.
2 + I = 3 + 4, so I = +5 A. It is positive, so it really flows into the junction.
4
At a junction 4 A flows in. Out of it flow 2 A and 1 A. A fourth wire is assumed to carry I into the junction. Find I and say what the sign means.
4 + I = 2 + 1, so I = −1 A. It is negative, so 1 A really flows out of the junction.
