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}} = V1 + V2 + V3 + \dots + V_n\$
⚡️ Tip: Remember, in series, current is constant but voltage divides.
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}} = I1 + I2 + I3 + \dots + I_n\$
⚡️ Tip: In parallel, voltage is constant but current divides.
📝 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}\$.
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:
| Configuration | Voltage Relationship | Current Relationship |
|---|---|---|
| Series | \$V{\text{total}} = \sum Vi\$ | \$I_{\text{total}} = I\$ (constant) |
| Parallel | \$V_{\text{total}} = V\$ (constant) | \$I{\text{total}} = \sum Ii\$ |
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).