Physics · Grades 9–12
Series and parallel: what stays the same
Use topology before choosing voltage and current rules.
Learn the idea
Series
Resistors in series carry the same current. Their resistances add in the ideal ohmic model.
Parallel
Parallel branches share the same potential difference. Branch currents add at a junction.
Equivalent resistance
For positive resistors in parallel, equivalent resistance is below the smallest branch resistance.
Idealization
Assume ideal wires and source unless internal resistance is specified. This is calculation practice, not a wiring guide.
Worked examples
Resistors 4 Ω and 6 Ω are in series. Find equivalent resistance.
Series resistances add: 4 + 6 = 10 Ω.
10 Ω
Two 8 Ω resistors are in parallel. Find equivalent resistance.
Equal resistors in parallel give R/2 = 4 Ω.
4 Ω
Check your understanding
What is equal across parallel branches connected to the same two nodes?
- Every branch resistance
- Every branch current regardless of resistance
- Potential difference
Parallel branch currents are 0.4 A and 0.7 A. Find total source current.
Why is adding two parallel resistances directly incorrect?
Answers and marking notes
Answers and marking notes
- Potential difference
They share the same pair of electrical potentials.
- 1.1 A
Currents add at the junction: 0.4 + 0.7 = 1.1 A.
- Their conductances add; use reciprocals or a valid equivalent relationship.
Credit topology-specific calculation.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.