Know that the current at every point in a series circuit is the same
4.3.2 Series and Parallel Circuits
Key Concept: Current in a Series Circuit
In a series circuit, the current is the same at every point along the path. Think of it like a single water pipe: no matter where you look, the same amount of water flows through each section. Similarly, electrons travel through each component one after another, so the flow (current) cannot change.
Mathematically, if a battery supplies a voltage \(V\) and the circuit contains resistors \(R_1, R_2, \dots, R_n\), the total resistance is \[ R_{\text{total}} = R_1 + R_2 + \dots + R_n \] and the current is \[ I = \frac{V}{R_{\text{total}}}. \] This current \(I\) flows through every resistor.
Analogy: Water Flow
• Series circuit: Imagine a single garden hose with a few small holes (resistors). Water (current) flows through each hole in the same amount. • Parallel circuit: Imagine a split hose where water can choose different paths. The total water flow splits, so each branch gets a part of the flow.
Example: Simple Series Circuit
A 9 V battery powers two resistors in series: \(R_1 = 3\,\Omega\) and \(R_2 = 6\,\Omega\).
• Total resistance: \(R_{\text{total}} = 3 + 6 = 9\,\Omega\).
• Current: \(I = \frac{9\,\text{V}}{9\,\Omega} = 1\,\text{A}\).
• The same 1 A flows through both \(R_1\) and \(R_2\).
• Voltage drop across \(R_1\): \(V_1 = I R_1 = 1\,\text{A} \times 3\,\Omega = 3\,\text{V}\).
• Voltage drop across \(R_2\): \(V_2 = I R_2 = 1\,\text{A} \times 6\,\Omega = 6\,\text{V}\).
• Check: \(V_1 + V_2 = 3\,\text{V} + 6\,\text{V} = 9\,\text{V}\) (matches battery voltage).
Series vs Parallel Summary
| Feature | Series | Parallel |
|---|---|---|
| Current | Same at every point | Splits among branches |
| Voltage | Drops across each component | Same across each branch |
| Total Resistance | \(R_{\text{total}} = \sum R_i\) | \(1/R_{\text{total}} = \sum 1/R_i\) |
Exam Tips 🚀
- Remember: current is constant in series – always check the circuit diagram first.
- When asked for total resistance in series, simply add the resistances.
- Use Ohm’s law \(V = IR\) to find missing values; keep units consistent.
- For parallel circuits, reciprocal rule for resistances: \(1/R_{\text{total}} = 1/R_1 + 1/R_2 + \dots\).
- Practice drawing clear circuit diagrams; label all components and values.
Revision
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