A series-parallel circuit is a combined circuit in which some components are arranged in the series configuration while other components are arranged in a parallel configuration.

Figure 1: A Series-Parallel circuit

How to find Equivalent resistance

  1. First of all, identify the series components
  2. After this identify the parallel components
  3. Solve series components
  4. Solve parallel components
  5. Replace the series resistors by the new equivalent resistance
  6. Replace parallel resistors by the new equivalent resistance
  7. Again solve all components to obtain equivalent resistance

Let’s solve the example of figure 1.

Step 1: R1 and R2 are in series

Step 2: R3, R4, and R5 are in parallel

Step 3: Req (s) = R1 + R2 = 5 + 5 = 10 ohms

Step 4: Req (p) = 1/((1/R1) + (1/R2) + (1/R3)) = 1/((1/9) + (1/9) + (1/9)); Req = 3 ohms

Step 5 & 6: Finally Req (s) and Req (p) are in series

Step 7: Solving Req (s) and Req (p) in series yields final equivalent resistance of 13 ohms.

Req = Req (s) + Req (p) = 10 + 3 = 13 ohms