Series and parallel circuits
There are two basic ways to connect parts in a circuit. In series, parts sit one after the other on a single path: the same current flows through each, resistances add and the battery's voltage splits between them. In parallel, parts sit side by side on their own branches: each gets the full voltage, the currents add, and the combined resistance drops. Two boards with a 6 V battery and two bulbs each show both, with real numbers, Kirchhoff's two laws, and why the sockets in a house are wired in parallel.
5 quick questions
Pick an answer to see why. Your score saves with your progress.
01A 100 Ω bulb and a 200 Ω bulb are in series on a 6 V battery. What is the total resistance?
In series the current has to get through both parts, so the resistances add: 100 Ω + 200 Ω = 300 Ω. Ohm's law then gives the current: 6 V ÷ 300 Ω = 20 mA.
02In that series circuit, 20 mA flows. What voltage does the 200 Ω bulb use?
V = I × R = 0.02 A × 200 Ω = 4 V. The 100 Ω bulb uses the other 2 V. The bigger resistance takes the bigger share of the voltage: a voltage divider.
03What is the combined resistance of two 100 Ω bulbs in parallel?
1/R = 1/100 + 1/100 = 2/100, so R = 50 Ω. Each branch is another path for the current, so the combined resistance is always less than the smallest branch.
04120 mA flows into a junction. One branch takes 60 mA. How much flows down the other branch?
Kirchhoff's current law: the current flowing into a junction equals the current flowing out. 120 mA in = 60 mA + 60 mA out. Charge is never made or lost at a junction.
05Why are the sockets in a house wired in parallel rather than in series?
In parallel every socket sits across the same supply, so each gets the full mains voltage (about 230 V in Europe, 120 V in North America) and switching one appliance off does not affect the others. In series, one gap would stop every appliance.
Glossary
- Series circuit
- Parts connected one after the other on a single path, so the same current flows through every part.
- Parallel circuit
- Parts connected side by side on separate branches, so every branch has the same voltage across it.
- Branch
- One of the separate paths in a parallel circuit.
- Junction
- A point where three or more wires meet, so the current can split or join.
- Resistance (Ω)
- How hard a part resists the flow of current, measured in ohms.
- Voltage divider
- Two or more resistances in series that share a voltage in proportion to their size.
- Kirchhoff's current law
- The current flowing into a junction equals the current flowing out of it.
- Kirchhoff's voltage law
- Round any closed loop, the voltage gained (from the battery) equals the voltage used (by the parts).
Notes and sources
- The boards are a teaching model: an ideal 6 V battery, wires with no resistance, and each bulb treated as a fixed resistor. A real bulb's filament has a higher resistance when it is hot than when it is cold.
- Series and parallel rules after OpenStax University Physics Volume 2, section 10.2; Kirchhoff's junction and loop rules after section 10.3.
- Current is drawn in the conventional direction, out of the battery's + side and back into its - side; the electrons in the wires drift the other way. In the figure the dashes move at a speed set by the current.
- Mains: 230 V nominal in IEC 60038 (used across Europe); about 120 V at US household outlets (HyperPhysics). House wiring adds fuses and breakers for safety, which this lesson leaves out.
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