Series and Parallel Circuits

Orientation

Lesson goal: analyse current, voltage, and equivalent resistance in series, parallel, and combined circuits.

Students should read the circuit structure before substituting into equations.

Core Content

Series resistors:

$$R_s = R_1 + R_2 + ...$$

Parallel resistors:

$$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + ...$$

Kirchhoff's laws:

$$\sum I_\text{in} = \sum I_\text{out}$$

$$\sum \Delta V_\text{loop} = 0$$

Concept Check

1. In a series circuit, current is:

   • A. the same through each component
   • B. zero after the first resistor
   • C. larger after each resistor
   • D. unrelated to the circuit

   Answer: A.

2. In a parallel circuit, voltage across each branch is:

   • A. the same
   • B. always zero
   • C. split equally regardless of resistance
   • D. impossible to measure

   Answer: A.

3. An ammeter should be connected:

   • A. in series
   • B. in parallel only
   • C. across the battery only
   • D. not in a circuit

   Answer: A.

Applied Practice

A 12 V source is connected to a 3 ohm resistor in series with a parallel pair of 6 ohm and 12 ohm resistors.

1. Parallel section:

   $$R_p = \left(\frac{1}{6}+\frac{1}{12}\right)^{-1}=4\ \Omega$$

2. Total resistance:

   $$R_\text{eq} = 3 + 4 = 7\ \Omega$$

3. Total current:

   $$I = \frac{12}{7}=1.71\ \text{A}$$

Final answer: total current is $1.71\ \text{A}$.

Deep Practice And Writing

Prompt: explain why a parallel equivalent resistance is lower than any single branch resistance.

Tutor Context

Tutor should first ask the student to mark series groups and parallel branches. Do not let the student start with random substitution.

Maintenance Loop

One circuit sketch: identify series/parallel groups, meter placement, and which quantity is shared.

Source Trace

This lesson is materialised from the eduKG custom Year 11 chapter, existing textbook section, roadmap lesson, and Module 4 sequence listed in source_refs.