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 \(R1, R2, \dots, R_n\), the total resistance is
\[
R{\text{total}} = R1 + R2 + \dots + Rn
\]
and the current is
\[
I = \frac{V}{R_{\text{total}}}.
\]
This current \(I\) flows through every resistor.
• 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.
A 9 V battery powers two resistors in series: \(R1 = 3\,\Omega\) and \(R2 = 6\,\Omega\).
• 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 \(R1\) and \(R2\).
• Voltage drop across \(R1\): \(V1 = I R_1 = 1\,\text{A} \times 3\,\Omega = 3\,\text{V}\).
• Voltage drop across \(R2\): \(V2 = I R_2 = 1\,\text{A} \times 6\,\Omega = 6\,\text{V}\).
• Check: \(V1 + V2 = 3\,\text{V} + 6\,\text{V} = 9\,\text{V}\) (matches battery voltage).
| Feature | Series | Parallel |
|---|---|---|
| Current | Same at every point | Splits among branches |
| Voltage | Drops across each component | Same across each branch |
| Total Resistance | \(R{\text{total}} = \sum Ri\) | \(1/R{\text{total}} = \sum 1/Ri\) |