[1], [2] Kirchhoff's circuit laws/rules (KCL) are 2 laws/equalities of current and potential difference (voltage) in circuits. (1845) Made by by German physicist Gustav Kirchhoff, which made Georg Ohm's work and preceded James Clerk Maxwell's.
equalities:
Fig 1
n = total branch number with currents flowing to/away from a node
Kirchhoff's current law (KCL)/Kirchhoff's junction rule says any circuit's node/junction has same current value flowing in and flowing out.
Current is a signed (positive/negative) quantity reflecting direction to/away from a node, this principle can be succinctly written by Fig 1:
succinctly: brief/clearly expressed
Current entering any junction equal current leaving junction. i2 + i3 = i1 + i4
KCLs originate from experimental results. Current law maybe viewed as an extension of the conservation of charge, since charge is the product of current and the time the current has been flowing. If the net charge in a region is constant, the current law will hold on the boundaries of the region.[2][3] This means that the current law relies on the fact that the net charge in the wires and components is constant.
[1] Kirchhoff's voltage law (KVL)/Kirchhoff's 2nd law/Kirchhoff's loop rule says the directed potential differences (voltages) sum around any closed loop is 0. Like KCL, written as:
All voltages' sum around a loop equals 0.
v1 + v2 + v3 + v4 = 0
If we connect a voltmeter at point 2 to 1, red test lead to point 2 and the black test lead to point 1, the meter would register +45 V.
“+” isn't shown, but implied, on positive readings in digital displays, except here to understand. A voltage has a double subscript (“2-1” in “E2-1”) means the voltage measured from point 2 to 1. A voltage specified as “Ecd” would mean the voltage as indicated by a digital meter with the red test lead on point “c” and the black test lead on point “d”: the voltage at “c” in reference to “d”.
Voltage written as “Ecd” means it's indicated by a digital meter with the red test lead at point “c” and the black test lead at “d”.
If the same voltmeter measures each resistor's voltage drop around the circuit in clockwise with the red test lead at a point ahead and the black test lead at the point behind, we get these readings:
E3-2 = -10 V,
E4-3 = -20 V,
E1-4 = -15 V
Measured voltages' sum equal 0:
Fig 3
This digital voltmeter shows across each component:
If the same voltmeter read voltage across component combinations, from R1 across, we see how voltages' sum equal 0 (Fig 3):
Fig 2
[3] KVL is for any circuit configuration, like parallels:
As a parallel circuit, voltage per resistor is the same as supply voltage: 6 V, from all all voltages 2, 3, 4, 5, 6, 7, 2:
As we started at point 2 and point 2, the voltages sum is the same as point E2-2 (= 0).
n = total voltages number measured
Consider an arbitrary circuit. Approximate the circuit by lumped elements, so each component has a time-varying magnetic fields and the field in the part outside to the circuit is negligible. By this assumption, the Maxwell–Faraday equation shows that
in the outside region. If each components has a finite volume, the outside region connects, so the electric field is conservative there. So, in any loop in the circuit,
with Pi as paths around the outside per components, from a terminal to another.
[Q1] Flashcard