use the formula for the combined resistance of two or more resistors in series
Kirchhoff’s Laws & Series Resistance
When you see a question about “combined resistance” in a series circuit, write the formula first:
$R_{\text{total}} = R_1 + R_2 + \dots + R_n$
What is a Series Circuit?
Think of a series circuit like a single water pipe that splits into several smaller pipes and then joins back together. All the water (current) flows through each pipe (resistor) one after the other, so the total resistance is the sum of all the individual resistances.
The Formula in Action
When resistors are connected end‑to‑end, the total resistance is:
$R_{\text{total}} = R_1 + R_2 + \dots + R_n$
| Resistor | Value (Ω) |
|---|---|
| $R_1$ | 100 |
| $R_2$ | 200 |
| $R_3$ | 300 |
| Total | 600 Ω |
Quick Example
🔌 Question: Three resistors of 50 Ω, 70 Ω and 120 Ω are connected in series. What is the total resistance?
?? Answer: $R_{\text{total}} = 50 + 70 + 120 = 240\,\Omega$.
Kirchhoff’s Current Law (KCL) Reminder
In a series circuit, the current is the same through every resistor. So if the battery supplies 2 A, each resistor carries 2 A.
Kirchhoff’s Voltage Law (KVL) Reminder
The sum of voltage drops across all resistors equals the supply voltage.
$$V_{\text{supply}} = V_{R_1} + V_{R_2} + \dots + V_{R_n}$$
Always double‑check that the resistors are indeed in series (no branching paths).
Common Mistakes to Avoid
- Mixing up series and parallel formulas.
- Assuming the same voltage across each resistor in series.
- Forgetting to include all resistors in the sum.
Practice Challenge
🔋 A 9 V battery is connected to four resistors in series: 10 Ω, 15 Ω, 25 Ω and 30 Ω.
1️⃣ Calculate the total resistance.
2️⃣ Find the current flowing through the circuit.
3️⃣ Determine the voltage drop across the 25 Ω resistor.
Use the formulas above to solve each part. Good luck! 🚀
Revision
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