Equivalent resistance — Science definition
The single resistance that could replace a whole combination of resistors and draw the same current.
Where it is taught
- Circuits & Ohm's Law — Electricity, Magnetism & Circuits, Physics & Environmental Science, Grade 12
Questions using equivalent resistance
Problem 1
Two 12 Ω resistors are connected in parallel. Find their equivalent resistance.
Answer and explanation
6 Ω
1/R = 1/12 + 1/12 = 2/12 = 1/6, so R = 6 Ω. (For two equal resistors, the parallel total is always half of one.)
Problem 2
Two 6 Ω resistors are in parallel across 12 V. Find equivalent resistance and total current. Show the reasoning, not just the conclusion.
Hints
Kirchhoff's loop balance provides a check.
Answer and explanation
R_eq=3 Ω; I_total=12/3=4 A, with 2 A per branch.
Problem 3
Two resistors 4 Ω and 12 Ω are in parallel across an ideal 12 V source. Find each current, total current, equivalent resistance and total power.
Answer and explanation
Currents are 3 A and 1 A; total 4 A. Req=12/4=3 Ω and P=12×4=48 W. Branch powers 36 W and 12 W sum consistently.
Currents are 3 A and 1 A; total 4 A.
Req=12/4=3 Ω and P=12×4=48 W.
Branch powers 36 W and 12 W sum consistently.
Response criteria
- Use the stated measurements or conditions, with correct units.
- Connect the result to the physical or environmental mechanism or evidence relationship.
- Identify the assumption, model limit or further evidence requested.
Problem 4
Independent chapter check: Two resistors4 Ω and12 Ω are in parallel across an ideal12 V source. Find each current, total current, equivalent resistance and total power.
Answer and explanation
Currents are3 A and1 A; total4 A. Req=12/4=3 Ω and P=12×4=48 W. Branch powers36 W and12 W sum consistently.
Currents are3 A and1 A; total4 A.
Req=12/4=3 Ω and P=12×4=48 W.
Branch powers36 W and12 W sum consistently.
Response criteria
- Use the stated measurements or conditions, with correct units.
- Connect the result to the physical or environmental mechanism or evidence relationship.
- Identify the assumption, model limit or further evidence requested.