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 = V₁ + V₂ + V₃ + ...

I_T = I₁ = I₂ = I₃ = ...

R_T = R₁ + R₂ + R₃ + ...

1/C_T = 1/C₁ + 1/C₂ + 1/C₃ + ...

L_T = L₁ + L₂ + L₃ + ...

Parallel circuit rules

V_T = V₁ = V₂ = V₃ = ...

I_T = I₁ + I₂ + I₃ + ...

1/R_T = 1/R₁ + 1/R₂ + 1/R₃ + ...

C_T = C₁ + C₂ + C₃ + ...

1/L_T = 1/L₁ + 1/L₂ + 1/L₃ + ...

Voltage division

V₁ = V_T ⋅ R₁ / (R₁+R₂+R₃+...)

Current division

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

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 = ε₀ ⋅ ε_r

ε₀ is the permittivity in vaccum.

ε_r is the relative permittivity or dialectric constant.

Current of capacitor

I_C(t) = C dV_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 dI_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

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