DC circuit laws

I = V / R

Joule's law

P = V · I = I 2 · R = V 2 / R

Series circuit rules

VT = V1 + V2 + V3 + ...

IT = I1 = I2 = I3 = ...

RT = R1 + R2 + R3 + ...

1/CT = 1/C1 + 1/C2 + 1/C3 + ...

LT = L1 + L2 + L3 + ...

Parallel circuit rules

VT = V1 = V2 = V3 = ...

IT = I1 + I2 + I3 + ...

1/RT = 1/R1 + 1/R2 + 1/R3 + ...

CT = C1 + C2 + C3 + ...

1/LT = 1/L1 + 1/L2 + 1/L3 + ...

Voltage division

V1 = VTR1 / (R1+R2+R3+...)

Current division

I1 = IT ⋅ (R2+R3+...) / (R1+R2+R3+...)

Kirchhoff's voltage law (KVL)

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

Vi = 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:

C = Q / V

Parallel plate capacitor

C = ε ⋅ A / l

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

Permittivity

ε = ε0 ⋅ εr

ε0 is the permittivity in vaccum.

εr is the relative permittivity or dialectric constant.

Current of capacitor

IC(t) = C dVC(t) / dt

Voltage of capacitor

VC(t) = VC(0) + 1/C IC(t)⋅dt

Voltage of capacitor

VL(t) = L dIL(t) / dt

Current of inductor

IL(t) = IL(0) + 1/LVL(t)⋅dt

WC = C⋅V 2 / 2

Energy of inductor

WL = L⋅I 2 / 2

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