Kirchhoff's Laws

Explore conservation of charge and energy using explicit current-arrow and voltage-sign conventions.

Current Law (KCL)

I₁ = 5A (In)I₂ = 3A (In)I₃ = 4A (Out)I₄ = 4A (Out)
∑ Iin = ∑ Iout
I₁ + I₂ = I₃ + I₄
5 + 3 = 4 + I₄

I₄ = (5 + 3) - 4 = 4 A
Convention: I₁ and I₂ are defined toward the node; I₃ and I₄ are defined away from it.
A negative result means the actual current points opposite the arrow you assumed.

Voltage Law (KVL)

+-Vₛ = 12V+-V₁ = 3V+-V₂ = 4V+-V₃ = 5V
∑ Vloop = 0
Clockwise traversal: +Vₛ - V₁ - V₂ - V₃ = 0
Vₛ - V₁ - V₂ - V₃ = 0
12 - 3 - 4 - V₃ = 0

V₃ = 12 - 3 - 4 = 5 V
Convention: the source is treated as a voltage rise and each resistor label is treated as a drop in the loop direction.
If a solved drop is negative, the true polarity is opposite the assumed sign.

Legend

→
Reference arrowDefines the assumed current or loop-traversal direction used in the equations.
+ / -
Voltage signMarks the assumed polarity across each source or resistor for KVL.
−
Negative resultA negative solved current or voltage means the true direction or polarity is opposite the assumed reference.