# DC circuit rules

## Ohm's law

*I* = V / R

## Joule's law

*P* = V · I = I^{ 2} ·* R* = V^{ 2} / R

## Series circuit rules

*V*_{T} = V_{1} + V_{2} + V_{3} + ...

*I*_{T} = I_{1} = I_{2} = I_{3} = ...

*R*_{T} = R_{1} + R_{2} + R_{3} + ...

1/*C*_{T} = 1/*C*_{1} + 1/*C*_{2} + 1/*C*_{3} + ...

*L*_{T} = L_{1} + L_{2} + L_{3} + ...

## Parallel circuit rules

*V*_{T} = V_{1} = V_{2} = V_{3} = ...

*I*_{T} = I_{1} + I_{2} + I_{3} + ...

1/*R*_{T} = 1/*R*_{1} + 1/*R*_{2} + 1/*R*_{3} + ...

*C*_{T} = C_{1} + C_{2} + C_{3} + ...

1/*L*_{T} = 1/*L*_{1} + 1/*L*_{2} + 1/*L*_{3} + ...

## Voltage division

*V*_{1} = V_{T} ⋅ R_{1} / (*R*_{1}+*R*_{2}+*R*_{3}+...)

## Current division

*I*_{1} = I_{T} ⋅ (*R*_{2}+R_{3}+...) / (*R*_{1}+*R*_{2}+*R*_{3}+...)

## Kirchhoff's voltage law (KVL)

The sum of voltage drops at a current loop is zero:

∑ V_{i} = 0

## Kirchhoff's current law (KCL)

The junction between several circuit elements is called a node.

The sum of the currents values at a node is zero:

## ∑ I_{i} = 0

## Capacitance

*C* = Q / V

## Parallel plate capacitor

*C* = ε ⋅ A / l

ε is the permittivity in farad per meter (F/m).

## Permittivity

ε = ε_{0} ⋅ ε_{r}

ε_{0} is the permittivity in vaccum.

ε_{r} is the relative permittivity or dialectric constant.

## Current of capacitor

*I*_{C}(t) = C d V_{C}(t) /
dt

## Voltage of capacitor

*V*_{C}(t) = V_{C}(0)*
+ * 1/*C* ∫* I*_{C}(t)⋅*dt*

## Voltage of inductor

*V*_{L}(t) = L d I_{L}(t) /
dt

## Current of inductor

*I*_{L}(t) = I_{L}(0)*
+ * 1/*L* ∫*V*_{L}(t)⋅*dt*

## Energy of capacitor

*W*_{C} = C⋅V ^{2} / 2

## Energy of inductor

*W*_{L} = L⋅I ^{2} / 2