Series and Parallel Component Calculations – Resistances, Inductances, Capacitances

Series and Parallel Resistances

When resistors are connected end‑to‑end, the total resistance is the arithmetic sum:

Series: R_eq = R₁ + R₂ + … + R_n

In a parallel arrangement, each resistor shares the same two nodes, reducing the overall resistance. The reciprocal of the equivalent resistance equals the sum of the reciprocals of the individual resistances:

Parallel: 1/R_eq = 1/R₁ + 1/R₂ + … + 1/R_n  ⇒ R_eq = 1 / (1/R₁ + 1/R₂ + … + 1/R_n)

Series and Parallel Inductances

Inductors behave like resistors with respect to magnetic flux linkage. In series, the magnetic fields add:

Series: L_eq = L₁ + L₂ + … + L_n

In parallel, the net inductance is less than any single inductor because the magnetic flux is shared:

Parallel: 1/L_eq = 1/L₁ + 1/L₂ + … + 1/L_n  ⇒ L_eq = 1 / (1/L₁ + 1/L₂ + … + 1/L_n)

Series and Parallel Capacitances

Capacitors store electric charge. When connected in series, the total capacitance decreases because the effective plate area is reduced:

Series: 1/C_eq = 1/C₁ + 1/C₂ + … + 1/C_n  ⇒ C_eq = 1 / (1/C₁ + 1/C₂ + … + 1/C_n)

In parallel, the total capacitance is simply the sum of individual capacitances, increasing the stored charge capacity:

Parallel: C_eq = C₁ + C₂ + … + C_n

RELATED WORKSHEETS:

• Series-Parallel DC Circuits Worksheet
• Series and Parallel AC Circuits Worksheet
• Series-Parallel Combination AC Circuits Worksheet