Kirchhoff's laws - Aetherwisp

Kirchhoff's laws are two empirical laws that describe the behavior of electric current and electric potential differences within circuits. They are consequences of the conservation of electric charge and the conservative nature of the electrostatic field respectively, and rely on the direction of current within the wire.

Kirchhoff's junction law#

Kirchhoff's first law, or Kirchhoff's junction law, states that the total directed sum of currents passing through a junction is always zero:

\sum_{i=1}^{N} I_{i}=0

By directed we mean that the sign of each current is plus if it is ingoing and negative if it is outgoing. In other words, the sum of entering currents in equal to the sum of exiting currents.

Kirchhoff's loop law#

Kirchhoff's second law, or Kirchhoff's loop law, states that the total directed sums of potential differences over a closed loop is always zero:

\sum_{i=1}^{N} \Delta V_{i}=0

By directed we mean that $\Delta V$ is positive if $V$ increases across a point or component and negative if it decreases.

In magnetic circuits#

Similar laws hold in magnetic circuits too, where the current is replaced by the flux of the magnetic field.

First law#

The total directed sum of the magnetic fluxes passing through a junction is always zero:

\sum_{i=1}^{N} \Phi_{B}=0

Second law#

The total directed sum of magnetic potential differences $\Delta V_{M}$ over a closed loop is always zero:

\sum_{i=1}^{N} \Delta V_{M}=0