Electric Power
Electric power is the rate at which electrical energy is transferred, converted, or dissipated by a circuit element. For a resistor, equivalent power expressions follow from combining P = IΔV with Ohm’s law.
Electric Power: quick answer
Electric power is the rate at which electrical energy is transferred, converted, or dissipated by a circuit element. For a resistor, equivalent power expressions follow from combining P = IΔV with Ohm’s law. Power answers an energy-rate question. The same resistor can show opposite resistance trends depending on what the rest of the circuit holds fixed, so strong reasoning states the constraint before selecting P=I²R or P=(ΔV)²/R.
Before predicting how power changes when resistance changes, identify whether current or potential difference is being held fixed; the conclusion reverses between those constraints.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at worked examples.
Use P=IΔV for energy-transfer rate.
Derive and use resistor forms P=I²R and P=(ΔV)²/R.
Predict bulb brightness qualitatively from power.
Compare power after circuit changes by first identifying which quantities remain fixed.
Key terms you need for this lesson
Definitions stay beside the circuit model so unfamiliar terminology does not break the reasoning chain.
electric power
electric power is the rate at which electrical energy is transferred, converted, or dissipated.
joule heating
joule heating is conversion of electrical energy into thermal energy in a resistive element.
power dissipation
power dissipation is energy converted per unit time by an element, often into thermal energy.
brightness
brightness is for otherwise comparable bulbs, a qualitative indicator that increases with electrical power.
watt
watt is the SI unit of power, equal to one joule per second.
constraint
constraint is a quantity or condition held fixed while another parameter changes.
Know what each relationship means and when it applies
The relationship, variables, topology condition, and physical anchor belong together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
P = IΔV | P power (W = J/s); I current (A); ΔV potential difference (V) | any circuit element when current and potential difference are known | 12 V across a device carrying 2 A corresponds to 24 W |
P = I²R | P power (W); I current (A); R resistance (Ω) | resistive element with current known | at fixed current, doubling R doubles power |
P = (ΔV)²/R | P power (W); ΔV potential difference (V); R resistance (Ω) | resistive element with potential difference known | at fixed voltage, doubling R halves power |
What a strong circuit diagram or graph must show
Translate the same physical model among topology, arrows, graphs, equations, and energy/charge reasoning.
Energy-flow diagram
source transfers energy electrically; resistor/bulb converts it to thermal/light energy.
P-versus-I at fixed R
upward-curving quadratic dependence from P=I²R.
P-versus-ΔV at fixed R
upward-curving quadratic dependence from P=(ΔV)²/R.
Bulb comparison
greater electrical power corresponds qualitatively to greater brightness for comparable bulbs.
Change one circuit condition and inspect what responds
Make a prediction before moving a control, then explain the output using topology, conservation, or the governing relationship.
Two examples with the model choice shown
The solution exposes the circuit reasoning pathway rather than only the arithmetic.
Device power
Situation: A circuit element has 9.0 V across it and carries 0.40 A.
Reasoning: Use P=IΔV because both current and potential difference are known.
P=0.40×9.0=3.6 W.
Resistance change at fixed voltage
Situation: Two resistors are separately connected across the same ideal 12 V source; one has twice the resistance of the other.
Reasoning: At fixed ΔV, P=(ΔV)²/R, so power is inversely proportional to resistance.
The resistor with twice the resistance dissipates half the power.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 11.4?
Use electric power when the question asks how quickly electrical energy is transferred or dissipated by a component.
How this idea fits the course
Power combines current from 11.1 with voltage/resistance from 11.3 and becomes an energy-rate check for compound circuits.
Scope check before solving
Before predicting how power changes when resistance changes, identify whether current or potential difference is being held fixed; the conclusion reverses between those constraints.
Turn this topic into measurable evidence
Choose variables and meters that test the intended relationship without accidentally changing the circuit model.
Investigation target
Measure voltage and current for several resistors, calculate power, and compare power with heating qualitatively.
Reasoning errors to eliminate
Repair the circuit model before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can identify the circuit topology before applying series/parallel formulas.
- I can define every electrical quantity and give its SI unit.
- I can distinguish charge conservation at junctions from energy conservation around loops.
- I can interpret current, potential, resistance, and power from a graph or schematic.
- I can place ideal meters correctly and predict qualitative loading effects of nonideal meters.
- I can design or critique a circuit experiment and justify a claim from measured evidence.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 11.4 FAQs
What is the safest power equation?
P=IΔV is the general circuit-element relation; resistor-specific forms follow from Ohm’s law.
Why are there three power formulas?
For an ohmic resistor they are algebraically equivalent, but different forms expose different controlled-variable reasoning.
How is bulb brightness related to power?
For comparable bulbs, more electrical power generally means greater brightness.
Does higher resistance mean more heating?
Only after you state the constraint. At fixed current, yes; at fixed voltage, power decreases as resistance increases.
What is one watt?
One watt is one joule of energy transferred each second.
How is energy use related to power?
For constant power over time, energy transferred equals PΔt.