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ElectricityIntroStarter track

Concept module

Power and Energy in Circuits

Keep one source and one resistive load in view while current, power, and accumulated energy over time stay tied to the same honest circuit.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Time

0.00 s / 12.0 sLivePause to inspect a specific moment, then step or scrub through it.

0.00 s12.0 s

Power and Energy in Circuits

One source, one resistive load, one honest time axis. The glow, current flow, power readout, and cumulative energy bar all come from the same live circuit state instead of from separate teaching widgets.

Graphs

Switch graph views without breaking the live stage and time link.

Energy transferred over time

Follow one fixed setup through time. The slope of the line is the current power, so steeper lines mean the circuit is transferring energy more quickly.

time (s): 0 to 12energy transferred (J): 0 to 256

Delivered energy

Hover or scrub to link the graph back to the stage.time (s) / energy transferred (J)

Controls

Adjust the physical parameters and watch the motion respond.

Source voltage

V

12 V

Raises or lowers the source push without changing the load itself.

Load resistance

R_{load}

8 ohm

Changes how strongly the load limits current in this bounded ohmic-circuit model.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

Graph readingPrompt 1 of 1

On the energy graph, the slope is the power. A steeper line means the circuit is transferring more energy each second, not just more total energy because more time passed.

Try this

Pause the run, compare the line slope for the steady-glow and low-resistance-heater setups, then read the stage power bar.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

V

Source voltage

12 V

Raises the push from the source. At fixed load resistance it increases current and makes the power curve bend upward faster than the current line.

Graph: Energy transferred over timeGraph: Current vs source voltageGraph: Power vs source voltageOverlay: Current arrowsOverlay: Voltage labelsOverlay: Power glowOverlay: Energy meter

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use the current prompt as a compact investigation cue. Each one points at a pattern the stage and graphs already show in the live circuit.

Graph readingPrompt 1 of 1

Graph: Energy transferred over time

On the energy graph, the slope is the power. A steeper line means the circuit is transferring more energy each second, not just more total energy because more time passed.

Try this

Pause the run, compare the line slope for the steady-glow and low-resistance-heater setups, then read the stage power bar.

Why it matters

This is the cleanest way to separate power from energy without leaving the same circuit.

Control: Source voltageControl: Load resistanceGraph: Energy transferred over timeOverlay: Power glowOverlay: Energy meter

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

4 visible

Overlay focus

Current arrows

Shows the one-loop current direction and the live current label on the wire.

What to notice

For one fixed load, current changes immediately when voltage or resistance changes.

Why it matters

Power only makes sense once the current stays tied to the same visible circuit.

Control: Source voltageControl: Load resistanceGraph: Current vs source voltageGraph: Power vs source voltageEquation

V

Equation

R_{load}

Challenge mode

Use the same single-load circuit for compact power targets. The checklist reads the live current and power, so rate and total stay tied to one honest setup.

0/1 solved

TargetCore

6 of 7 checks

Steady 18-watt load

Starting from Gentle glow, keep the 8 ohm load and raise the source until the stage power bar settles near 18 W.

Graph-linkedGuided start2 hints

Suggested start

Use the power-voltage graph and the stage power bar together while you raise the source.

Pending

Open the Power vs source voltage graph.

Energy transferred over time

Matched

Keep the Power glow visible.

Matched

Keep the Current arrows visible.

Matched

Keep voltage between 11.8 V and 12.2 V.

12 V

Matched

Keep load resistance between 7.8 ohm and 8.2 ohm.

8 ohm

Matched

Keep current between 1.45 A and 1.55 A.

1.5 A

Matched

Keep power between 17.5 W and 18.5 W.

18 W

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

At t = 0 s, a 12 V source drives a 8 ohm load. The current is 1.5 A, so the load power is 18 W and the delivered energy is 0 J. The load is dissipating power quickly enough that its visible response is strong but still controlled.

Equation detailsDeeper interpretation, notes, and worked variable context.

Ohm's law for the load

With one source and one ohmic load, current is set by the source voltage and the load resistance.

I = \frac{V}{R _{load}}

V

Source voltage 12 V

R_{load}

Load resistance 8 ohm

Electrical power

Power is the rate of electrical energy transfer right now.

P = V I

V

Source voltage 12 V

Power from source voltage

At fixed resistance, power rises with the square of voltage.

P = \frac{V ^{2}}{R _{load}}

V

Source voltage 12 V

R_{load}

Load resistance 8 ohm

Power from current

At fixed resistance, larger current means much larger power.

P = I^{2} R_{load}

R_{load}

Load resistance 8 ohm

Energy over time

Energy accumulates as the current power rate continues for more time.

E = P t

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 1 compact task ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Starter track

Step 4 of 60 / 6 complete

Electricity

Earlier steps still set up Power and Energy in Circuits.

1. Electric Fields2. Electric Potential3. Basic Circuits4. Power and Energy in Circuits+2 more steps

Previous step: Basic Circuits.

Start from track beginning

Short explanation

What the system is doing

Electrical power tells you how quickly a circuit is transferring energy right now. In one bounded resistive circuit, that rate comes straight from the same voltage, current, and resistance you already use in Ohm's law.

This page keeps the model intentionally small: one source drives one resistive load. That is enough to show how current changes with voltage and resistance, why the load brightens or heats more when power rises, and how energy keeps accumulating over time while the power stays fixed for one chosen setup.

Key ideas

01Power is a rate, while energy is the total transferred after that rate acts for some time.

02At fixed resistance, current follows voltage linearly, but power rises faster because P = VI and I also changes with V.

03At fixed source voltage, increasing the load resistance lowers current and power in this ohmic-load model.

Live power checks

Solve the exact state on screen.

Use the current source setting, load setting, and inspected time directly. The same circuit state drives the stage, readout card, overlays, and graphs.

Live valuesFollowing current parameters

For the current source and load, what current flows and how much power is the load taking right now?

V

Source voltage

12 V

R_{load}

Load resistance

8 ohm

1. Start with Ohm's law for the one-loop load

I = \frac{V}{R _{load}}

2. Substitute the current source and load values

I = \frac{1}{2} 8

3. Compute the live current

That gives

I = 1.5

4. Use the power relation on the same live circuit

P = V I = 12 \times 1.5

5. Compute the load power

P = 18

Current and power

I = 1.5, P = 18

This is a moderate-power setup, so the load response is clear without pushing the circuit into the strongest settings.

Energy-over-time checkpoint

Two runs use the same 12 V source and the same 8 ohm load. One stays on for 3 s and the other stays on for 9 s. Which run transfers more energy, and what quantity does not change between the runs?

Prediction prompt

Predict whether the power changes or whether only the accumulated energy changes before you answer.

Check your reasoning

The 9 s run transfers three times as much energy because the load power stays the same and energy is power multiplied by time.

With voltage and resistance fixed, the current and power stay fixed too. Time does not change the rate itself here; it only gives that same rate more seconds to accumulate energy.

Common misconception

A larger resistance means the component is working harder, so it must always use more power.

For one fixed source voltage and one ohmic load, larger resistance limits the current more strongly.

Because both current and power fall in that case, the higher-resistance load actually transfers energy more slowly even though the resistance number is larger.

Quick test

Reasoning

Question 1 of 5

Answer from the live circuit logic, not from detached rules. Each question asks what the stage, meters, or linked graphs must mean.

Which statement best separates power from energy in this circuit?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows one battery on the left, one resistive load on the top wire, and one return path on the bottom wire. A readout card on the right reports the live source voltage, load resistance, current, power, accumulated energy, and a short qualitative state label for the load response.

Moving charge markers circulate around the loop to keep the current direction visible over time. Optional overlays add current arrows, source and load voltage labels, a power-rate bar tied to the load response, and an energy meter that accumulates as the run continues or as you scrub the time rail.

The model is intentionally bounded to one ohmic source-load loop. There are no capacitors, inductors, or nonlinear devices, so every displayed change stays tied to the same beginner-level relations among voltage, current, resistance, power, and energy over time.

Graph summary

The energy-transfer graph plots delivered energy against time for the current circuit. Hovering or scrubbing lets you inspect the same moment on the stage and the same cumulative-energy value on the graph.

The current-voltage and power-voltage graphs sweep source voltage while the load stays fixed, so they show the different current and power responses clearly. The power-resistance graph sweeps only load resistance at one fixed source voltage to show why larger resistance lowers power in this bounded model.

Keep the circuit story going

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

See how branch structure changes powerElectricity

Power and Energy in Circuits

See each variable before you move it.

Current arrows

Steady 18-watt load

Electricity

What the system is doing

Solve the exact state on screen.

For the current source and load, what current flows and how much power is the load taking right now?

Which statement best separates power from energy in this circuit?

Keep moving through the concept map.

Series and Parallel Circuits

Equivalent Resistance

Electric Potential