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.

## How to find Equivalent resistance

- First of all, identify the series components
- After this identify the parallel components
- Solve series components
- Solve parallel components
- Replace the series resistors by the new equivalent resistance
- Replace parallel resistors by the new equivalent resistance
- 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