Series and parallel circuits
Track current and potential difference using two basic circuit arrangements.
Before you begin
- Current and voltage
- Ohm's law for a resistor
Use the single path in series
Components in series carry the same current because there is one unbranched path. Their potential differences add to the supply voltage. For resistors, their resistances add. A resistor's potential difference is V = IR under conditions where its resistance can be treated as constant. Adding series resistance reduces current for a fixed supply voltage.
Use shared voltage in parallel
Parallel branches connect across the same two points, so they have the same potential difference. The current splits among branches and recombines; branch currents sum to the total. Adding another resistive branch lowers the equivalent resistance and increases total current for an ideal fixed-voltage supply. Analyse mains electricity only theoretically here; do not build mains circuits.
Worked example
A 2 Ω resistor and a 4 Ω resistor are in series across 12 V. Find the current.
Show the worked solution
- Add the series resistances: 2 + 4 = 6 Ω.
- Apply I = V/R to the complete circuit: 12/6 = 2 A.
- The same 2 A passes through each resistor; their voltages are 4 V and 8 V.
2 A.
Try it yourself
Two 6 Ω resistors are in parallel across 12 V. What is the total current?
Common mistakes
- Parallel branches share voltage, not necessarily equal current.
What can you explain now?
Find the equivalent resistance of 4 Ω and 12 Ω connected in parallel.
Compare with the explanation
3 Ω.
1/R = 1/4 + 1/12 = 1/3, so R = 3 Ω. It is less than either branch resistance, as expected.
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