# 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 capacitor

*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