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:
$$\sum I_\text{in} = \sum I_\text{out}$$
$$\sum \Delta V_\text{loop} = 0$$
| Circuit type | Current | Voltage | Resistance |
|---|---|---|---|
| series | same through components | divides across components | adds |
| parallel | splits between branches | same across branches | reciprocal sum; lower than smallest branch |
Concept Check
-
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.
-
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.
-
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.
-
Parallel section:
$$R_p = \left(\frac{1}{6}+\frac{1}{12}\right)^{-1}=4\ \Omega$$
-
Total resistance:
$$R_\text{eq} = 3 + 4 = 7\ \Omega$$
-
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.
Maintenance Loop
One circuit sketch: identify series/parallel groups, meter placement, and which quantity is shared.