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ElectricityIntroStarter track

Concept module

Basic Circuits

Keep one battery and two resistors in view while current, voltage, resistance, Ohm's law, and the contrast between series and parallel all stay tied to one honest circuit.

Interactive lab

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

Basic Circuits

Keep the battery and two resistors fixed, then switch between one series loop and two parallel branches without turning this into an electronics workbench. The same readouts, overlays, compare mode, and graphs all come from that one bounded circuit.

Graphs

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

Ohm's law current map

Sweep the battery voltage while keeping the resistor values and topology fixed. Straight lines show how Ohm's law turns one fixed resistance setup into a linear current response.

battery voltage (V): 0 to 18current (A): 0 to 2

Total currentBranch A currentBranch B current

Hover or scrub to link the graph back to the stage.battery voltage (V) / current (A)

Controls

Adjust the physical parameters and watch the motion respond.

Battery voltage

V

12 V

Increase the push from the battery without changing the resistor values.

Resistor A

R_{A}

6 ohm

Sets the amber resistance in either the series loop or the upper parallel branch.

Resistor B

R_{B}

6 ohm

Sets the blue resistance and lets you test both unequal series division and unequal parallel current splits.

Use parallel branchesOff keeps one series loop. On splits the load into two branches across the same battery.

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

With one fixed topology and resistance setup, the current map stays linear because current is proportional to voltage.

Try this

Open the current map, hover a lower voltage and then a higher voltage, and compare how every current label on the stage scales with the same straight-line trend.

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

Battery voltage

12 V

Raises or lowers every current in the circuit without changing the resistor values themselves.

Graph: Ohm's law current mapGraph: Voltage share vs resistor BOverlay: Current arrowsOverlay: Voltage drops

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 circuit and graphs already show in the live state.

Graph readingPrompt 1 of 1

Graph: Ohm's law current map

With one fixed topology and resistance setup, the current map stays linear because current is proportional to voltage.

Try this

Open the current map, hover a lower voltage and then a higher voltage, and compare how every current label on the stage scales with the same straight-line trend.

Why it matters

This is the cleanest visual form of Ohm's law before extra circuit complexity is added.

Control: Battery voltageGraph: Ohm's law current mapOverlay: Current arrowsEquation

V

Guided overlays

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

2 visible

Overlay focus

Current arrows

Shows the total current and the branch currents directly on the circuit.

What to notice

Series shows one loop current everywhere, while parallel shows one total current that splits into branch currents and recombines.

Why it matters

Current direction and current sharing stay tied to one honest circuit instead of drifting into disconnected numbers.

Control: Battery voltageControl: Resistor AControl: Resistor BControl: Use parallel branchesGraph: Ohm's law current mapEquation

V

Equation

R_{A}

Equation

R_{B}

Challenge mode

Use the same compact battery-resistor model for honest circuit targets. The checklist reads the live branch voltages and total current from the actual stage.

0/1 solved

TargetCore

3 of 8 checks

Full-voltage parallel pair

Starting from the matched series pair, change only the circuit structure needed to give each branch the full battery voltage and make the total current land near 4 A.

Graph-linkedGuided start2 hints

Suggested start

Use the voltage-share graph and the node guide together while you rewire the equal pair.

Pending

Open the Voltage share vs resistor B graph.

Ohm's law current map

Matched

Keep the Current arrows visible.

Pending

Keep the Node guide visible.

Off

Matched

Keep resistance a between 5.8 ohm and 6.2 ohm.

6 ohm

Matched

Keep resistance b between 5.8 ohm and 6.2 ohm.

6 ohm

Pending

Keep equivalent resistance between 2.9 ohm and 3.1 ohm.

12 ohm

Pending

Keep total current between 3.9 A and 4.1 A.

1 A

Pending

Keep branch bvoltage between 11.8 V and 12.2 V.

6 V

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

A 12 V battery drives resistor A = 6 ohm and resistor B = 6 ohm. The equivalent resistance is 12 ohm, so the total current is 1 A. The circuit is in series, so the same current flows through both resistors. Branch A drops 6 V and Branch B drops 6 V. Both resistors dissipate similar power right now.

Equation detailsDeeper interpretation, notes, and worked variable context.

Ohm's law

For one fixed resistance, current grows in direct proportion to voltage.

I = \frac{V}{R}

V

Battery voltage 12 V

Series equivalent resistance

Two series resistors act like one larger resistor because the same loop current must pass through both.

R_{eq} = R_{A} + R_{B}

R_{A}

Resistor A 6 ohm

R_{B}

Resistor B 6 ohm

Parallel equivalent resistance

Two parallel branches lower the one-number load because charge has two paths across the same battery.

R_{eq} = \frac{R _{A} R _{B}}{R _{A} + R _{B}}

R_{A}

Resistor A 6 ohm

R_{B}

Resistor B 6 ohm

Same current in series

A steady series loop carries one current everywhere around the loop.

I_{A} = I_{B} = I_{total}

Current splits and recombines

In parallel, branch currents add back together at the junction.

I_{total} = I_{A} + I_{B}

Resistor voltage drop

Voltage across one resistor depends on the current through that resistor and the resistance of that element.

V_{drop} = I R

V

Battery voltage 12 V

R_{A}

Resistor A 6 ohm

R_{B}

Resistor B 6 ohm

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 3 of 60 / 6 complete

Electricity

Earlier steps still set up Basic Circuits.

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

Previous step: Electric Potential.

Start from track beginning

Short explanation

What the system is doing

A basic circuit needs only a source of voltage, a path for charge to move, and resistance that limits how much current the source can drive. Ohm's law connects those three ideas with one compact rule: more voltage pushes more current, and more resistance holds that current back.

This module stays intentionally bounded. One battery drives two resistors, and the only topology change is whether those resistors sit in one series loop or in two parallel branches. That is enough to teach current, voltage, equivalent resistance, and the intuition behind Ohm's law without turning the page into an electronics workbench.

Key ideas

01For one fixed circuit, Ohm's law means current scales linearly with voltage and inversely with equivalent resistance.

02In series, the same current flows through every resistor because there is only one loop, so resistances add and the source voltage is shared across the resistors.

03In parallel, each branch sees the full battery voltage, so branch currents depend on branch resistance and the total current is the sum of those branch currents.

Live circuit checks

Solve the exact state on screen.

Solve the circuit that is on screen right now. The same battery value, resistor values, and topology drive the stage, the readout card, the overlays, and the graphs.

Live valuesFollowing current parameters

For the current circuit, what one-number equivalent resistance does the battery feel, and what total current follows from that load?

V

Battery voltage

12 V

R_{A}

Resistor A

6 ohm

R_{B}

Resistor B

6 ohm

1. Start with the live topology

This setup uses series loop, so

R_{eq} = R_{A} + R_{B}

2. Substitute the resistor values now on screen

With

R_{A} = 6

and

R_{B} = 6

R_{eq} = 6 + 6

, so

R_{eq} = 12

3. Use Ohm's law on the whole circuit

I_{total} = \frac{V}{R _{eq}} = \frac{1}{2} 12

4. Compute the total current

That gives

I_{total} = 1

Equivalent resistance and total current

R_{eq} = 12, I_{total} = 1

Series resistances add directly, so each extra ohm raises the one-number load and reduces the same loop current everywhere.

Current-split checkpoint

Use the matched-resistor presets. Why does the total current become larger in the parallel circuit than in the series circuit even though the same battery and the same two resistors are still present?

Prediction prompt

Predict whether the battery is seeing more resistance or less resistance before you switch the topology.

Check your reasoning

The parallel circuit gives the battery a smaller equivalent resistance because the charge has two paths instead of one long path. With the same battery voltage, Ohm's law then gives a larger total current.

Series adds resistances directly, so two 6 ohm resistors become 12 ohm. Parallel combines them into 3 ohm, which is a much lighter load on the same battery. Lower equivalent resistance means higher total current.

Common misconception

Current gets used up by the first resistor, so less current reaches the second resistor in a series loop.

Current is the rate of charge flow through one continuous loop. In a steady series circuit, the same amount of charge per second passes every point in that loop.

What changes across a resistor is voltage, not the amount of current that remains. The resistor creates a voltage drop while the loop current stays the same.

Quick test

Reasoning

Question 1 of 5

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

A battery drives two resistors in one steady series loop. Which statement about the current is correct?

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 and two resistor blocks arranged either in one series loop or in two parallel branches. A readout card on the right reports the live battery voltage, resistor values, equivalent resistance, total current, branch currents, and branch voltages.

Optional overlays add current arrows on the wires, voltage labels on the battery and resistors, and node markers that show when two branches share the same top and bottom nodes. Compare mode adds a dashed ghost circuit for the second setup so topology or resistor changes stay visible without changing the main stage.

The stage is intentionally bounded to one battery and two resistors. There are no capacitors, switches, or symbolic solvers, so every displayed change stays tied to the same beginner-friendly current, voltage, and resistance logic.

Graph summary

The Ohm's law current map plots total current, branch A current, and branch B current against battery voltage for the current resistor setup and topology. Hovering the graph previews a different battery voltage on the stage without changing the actual controls.

The voltage-share graph sweeps only resistor B while holding the battery and resistor A fixed. In series it shows how the source voltage is divided, and in parallel it shows that both branches stay pinned to the full battery voltage even as the branch currents differ.

Keep the electricity story moving

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 rate and total in the same loopElectricity

Basic Circuits

See each variable before you move it.

Current arrows

Full-voltage parallel pair

Electricity

What the system is doing

Solve the exact state on screen.

For the current circuit, what one-number equivalent resistance does the battery feel, and what total current follows from that load?

A battery drives two resistors in one steady series loop. Which statement about the current is correct?

Keep moving through the concept map.

Power and Energy in Circuits

Series and Parallel Circuits

Equivalent Resistance