This section discusses the fundamental laws of electronic.

# 8.7. Kirchhoff’s circuit laws¶

Kirchhoff’s circuit laws are two equalities that constrain the current and voltage in electrical circuits under some approximations.

Kirchhoff’s current law (KCL) says at any node in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node:

$\sum_{k=1}^n {I}_k = 0$

This law is in fact a general principle of flux conservation.

Kirchhoff’s voltage law (KVL) says that the sum of the branch’s voltage along a closed path in the network is null:

$\sum_{k=1}^n {V}_k = 0$

Kirchhoff’s circuit laws are used by Spice to evaluate the voltages and currents in a circuit.

To go further on theses equalities, you can read online the section 22-3 of the Feynman Lectures on Physics, Volume II.

# 8.8. Ohm’s Law¶

The Ohm’s law is a simple model of a resistor which say that the current I flowing through a resistor is proportional to the voltage U applied accross it, this constant is called the resistance (R).

$U = R I$

You will observe the same phenomenum with a pipe filled with water, the water’s flow is proportional to the declination of the pipe, more you incline the pipe, more you pressure the water within the pipe. Electron act as water and voltage as pressure.

In reallity the resistance depends of the temperature of the material, like many device parameters. It is why we always simulate a circuit at a given temperature.

This law is important in circuit analysis, because it is a first approximation of any dipole for a particular current and voltage. Indeed we can approximate any curve locally by a linear relation. If we know the current and voltage of a dipole under some conditions then we can approximate the rate of change under a small variation of the current or voltage. Spice use this principle to evalute a circuit at different times.

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