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Inductance and Capacitance in Series and Parallel

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Equivalent Circuits

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Typically, electrical components are arranged in either series or parallel, and the following provides methods of which to simplify circuit arrangements involving inductors and capacitors.

Inductance in Series

v = v1 + v2 + • • • + vn = (L1 + L2 + • • • + Ln)

di dt

The equivalent inductance equals the sum of each inductance in series,
L_eq = L₁ + L₂ + • • • + L_n

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Inductance in Parallel

Leq   =

1 1 L1 + 1 L2 + • • • + 1 Ln

i = i₁ + i₂ + • • • + i_n
or,
i(t₀) = i₁(t₀) + i₂(t₀) + • • • + i_n(t₀)

For a single inductor:

i =

1 Leq

∫

t   t0

v dτ + i(t0)

(Eq. 1)

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Capacitance in Series

Ceq   =

1 1 C1 + 1 C2 + • • • + 1 Cn

v(t₀) = v₁(t₀) + v₂(t₀) + • • • + v_n(t₀)

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Capacitance in Parallel

C_eq = C₁ + C₂ + • • • + C_n

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Related
▪ L - Inductors