Short on time? This page is the recap. For explanations, the potential graph and the worked examples, use the full study guide.
Recap
- A charge q moving through a potential difference ΔV changes its electric potential energy by qΔV.
- Batteries turn non-electric energy into electric potential energy of the charges; resistors turn it into thermal energy.
- A point has one value of potential, so going round a closed loop and back to the start gives a total change of zero. That is the loop rule, and it is energy conservation.
- The rule holds for every closed loop, including loops with no battery. Such a loop shows that parallel branches have equal potential differences.
- The direction you go round the loop does not matter, as long as you keep it.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| ΔV = ΔU_E / q | V = J/C | link potential difference to energy per charge |
| ΣΔV = 0 | sum round one closed loop | write a loop equation |
| +ℰ / −ℰ | battery crossed − to + / + to − | sign of a battery term |
| −IR / +IR | resistor crossed with / against the current | sign of a resistor term |
| ΔV_terminal = ℰ − Ir | loop rule applied to the battery alone | terminal voltage of a real battery |
Assumptions behind the numbers
- Wires and ammeters are ideal (no potential change across them) unless stated.
- One reference point is chosen as 0 V and kept throughout.
- Resistances are constant, so each resistor term is ±IR.
Mistakes to avoid
- Wrong resistor sign when going against the current. It is +IR.
- Leaving out the −Ir term for a real battery.
- Thinking position decides the share of voltage. In one loop, resistance does.
- Ignoring loops without a battery. They are often the shortest route to an unknown.
- Graph not closing. A potential–position graph must end at its starting value.
- Saying current is used up. Potential falls; the current in one loop is the same everywhere.
Quick self-check
- A 1.5 V ideal cell drives a current through two resistors in series. The first has 0.90 V across it. What is across the second? (0.60 V)
- You cross a 10 Ω resistor against a current of 0.20 A. What is the term in your loop equation? (+2.0 V)
- 3.0 C of charge passes through a resistor with 4.0 V across it. How much electric potential energy does it lose? (12 J)
Next: practice questions.