Linear Circuit Analysis


Series Connections

Two or more components (each with two terminals) are connected in series when they are part of the same two minor meshes, or, to one minor mesh and the outside mesh. For instance, in Fig. 1:

  • Voltage source $V_1$ and resistor $R_1$ are connected in series because they both belong to minor mesh $i_1$ and the outside mesh.
  • Current source $I_1$ and capacitor $C_1$ are connected in series because they both belong to minor mesh $i_3$ and the outside mesh.
  • However, resistor $R_3$ and inductor $L_1$ are not connected in series because they belong to different pair of minor meshes (resistor $R_3$ belongs to $i_1$ and $i_2$, while inductor $L_1$ belongs to the outside mesh and $i_2$.
V1 R1 R2 L1 I1 C1 R3 v1 v2 v3 v4 v5 i1 i2 i3
Fig. 1. Example of a circuit with two series and one parallel connection.

In Fig. 2:

  • Voltage source $V_1$ and inductor $L_1$ are connected in series because they both belong to minor mesh $i_2$ and the outside mesh.
  • Capacitor $C_1$, current source $i_1$ and capacitor $C_2$ are connected in series because they all belong to minor mesh $i_3$ and the outside mesh.
  • Resistor $R_2$ and inductor $L_2$ are connected in series because they both belong to minor meshes $i_2$ and $i_3$.
V1 R1 R2 C1 L1 L2 I1 C2 C3 v1 v2 v3 v4 v5 v6 v7 i1 i2 i3
Fig. 2. Example of a circuit with with multiple series and parallel connections.

If one component is connected in series with a second component, and the second component is connected in series with the third component, then, the first component is also connected in series with the third component.

Parallel connections

Two or more components (each having two terminals) are connected in parallel when they are connected between the same two nodes. For instance, looking at the circuit in Fig. 2:

  • Capacitor $C_3$ and resistor $R_1$ are connected in parallel because they are both connected between nodes $v_2$ and $v_3$.
  • However, inductors $L_1$ and $L_2$ are not connected in parallel because they are not connected between the same two nodes (inductor $L_1$ is connected between $v_3$ and $v_6$, while inductor $L_2$ is connected between $v_4$ and $v_6$.

If one component is connected in parallel with a second component, and the second component is connected in parallel with the third component, then, the first component is also connected in parallel with the third component.

  • Identify series and parallel connections in electric networks
    1070
    1071
    1072
    1073
See also