Calculate the combined e.m.f. of several sources in series
4.3.2 Series and Parallel Circuits
What is a Series Circuit?
A series circuit is like a single line of people passing a ball. The ball (current) must travel through each person (component) one after another. If one person drops the ball, the whole line stops.
In electrical terms, the same current flows through every element, and the total voltage (e.m.f.) is the sum of the individual voltages:
$$V_{\text{total}} = V_1 + V_2 + V_3 + \dots + V_n$$⚡️ Tip: Remember, in series, current is constant but voltage divides.
What is a Parallel Circuit?
A parallel circuit is like a group of friends each holding a separate ball. Each friend can play independently; if one stops, the others keep playing.
In this case, the voltage across each branch is the same, but the total current is the sum of the currents in each branch:
$$I_{\text{total}} = I_1 + I_2 + I_3 + \dots + I_n$$⚡️ Tip: In parallel, voltage is constant but current divides.
Exam Tip: Calculating Combined e.m.f. in Series
- Identify all the voltage sources in the series branch.
- Use the formula: $V_{\text{total}} = \sum V_i$.
- Check the polarity: if a source is reversed, subtract its voltage.
- Write the final answer with the correct sign.
📝 Example: Two batteries, 3 V and 5 V, connected in series (same polarity). $V_{\text{total}} = 3\,\text{V} + 5\,\text{V} = 8\,\text{V}$.
Practice Problem
Three voltage sources are connected in series: a 2 V source, a 4 V source, and a 1 V source that is reversed (negative polarity). What is the combined e.m.f.?
Solution:
- Sum the voltages: $2\,\text{V} + 4\,\text{V} - 1\,\text{V} = 5\,\text{V}$.
- Answer: $V_{\text{total}} = 5\,\text{V}$.
Quick Reference Table
| Configuration | Voltage Relationship | Current Relationship |
|---|---|---|
| Series | $V_{\text{total}} = \sum V_i$ | $I_{\text{total}} = I$ (constant) |
| Parallel | $V_{\text{total}} = V$ (constant) | $I_{\text{total}} = \sum I_i$ |
Final Exam Hint
When you see a question about “combined e.m.f. of several sources in series,” remember: add all voltages, taking care of polarity. If a source is reversed, subtract its magnitude. Write the answer with the correct sign and unit (V).
Revision
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