Series and Parallel Networks with Kirchhoff’s Laws

Electrical Engineering · CHAPTER 2 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Reduce resistor networks and verify current and voltage balances.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

Series components carry the same current. Parallel branches share the same voltage. Kirchhoff’s current law balances currents at a node; the voltage law balances voltage changes around a closed loop in the lumped circuit approximation. Equivalent resistance is a model seen by the source.

2. Write the model

Rseries = R1 + R2; 1/Rparallel = 1/R1 + 1/R2

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

Two 100 Ω resistors in series across 12 V have 200 Ω total and draw 60 mA. In parallel they have 50 Ω total and draw 240 mA, with 120 mA in each branch.

4. Explore the model

Concept diagram: specify the case, evaluate its model, then verify against the scenario table.

Illustrative scenario sweep — synthetic educational data
Connection	Equivalent R (Ω)	Source current (mA)
One resistor	100	120
Two in series	200	60
Two in parallel	50	240

Compare topology while keeping component values and supply voltage fixed. Connectivity changes source current substantially.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

What is the parallel equivalent of two 200 Ω resistors?

Reveal the answer and check your work

100 Ω.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

Do not add parallel resistances directly.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.