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ElectricityIntroStarter track

Concept module

Series and Parallel Circuits

Switch the same two loads between one loop and two branches, then track how current, voltage, brightness, and charge flow reorganize without changing the battery.

Interactive lab

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

Time

0.00 s / 12.0 sLiveBranch-response graphs stay resistance-based while the time rail inspects live charge flow, branch counters, and brightness honestly.

0.00 s12.0 s

Series and Parallel Circuits

Keep the same battery and two loads on screen, then switch only the branch structure. Current, voltage, brightness, compare mode, and the response graphs all stay tied to that one bounded circuit.

Graphs

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

Branch current vs load B

Sweep only load B while keeping the battery, load A, and topology fixed. In series, every current falls together because one loop current crosses both loads. In parallel, load A stays fixed while load B and the total current respond to the changing branch resistance.

load B resistance (ohm): 2 to 18current (A): 0 to 2

Total currentLoad A currentLoad B current

Hover or scrub to link the graph back to the stage.load B resistance (ohm) / current (A)

Controls

Adjust the physical parameters and watch the motion respond.

Battery voltage

V

12 V

Raises or lowers the battery push for both arrangements.

Load A resistance

R_{A}

6 ohm

Sets the amber load in either the single series path or the upper parallel branch.

Load B resistance

R_{B}

6 ohm

Sets the blue load and makes branch-current and brightness differences visible.

Use parallel branchesOff keeps one series loop. On gives the same battery two separate branches.

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 branch-current graph, series keeps one current everywhere, while parallel lets branch B slide on its own and makes the total current follow the branch sum.

Try this

Open the branch-current graph, stay at 12 V, then drag only load B. In parallel, the amber branch line stays fixed while the blue and teal lines move.

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

Changes the push from the battery without changing the load arrangement itself.

Graph: Branch current vs load BGraph: Load voltage vs load BGraph: Load power vs load BOverlay: Current flowOverlay: Voltage labelsOverlay: Brightness guide

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 bounded circuit, overlays, and response graphs already show in the live state.

Graph readingPrompt 1 of 1

Graph: Branch current vs load B

On the branch-current graph, series keeps one current everywhere, while parallel lets branch B slide on its own and makes the total current follow the branch sum.

Try this

Open the branch-current graph, stay at 12 V, then drag only load B. In parallel, the amber branch line stays fixed while the blue and teal lines move.

Why it matters

Current splitting becomes something you can read directly instead of memorizing as a detached rule.

Control: Load B resistanceControl: Use parallel branchesGraph: Branch current vs load BOverlay: Current flowEquation

R_{B}

Guided overlays

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

3 visible

Overlay focus

Current flow

Shows the live current arrows and charge counters on the stage.

What to notice

Series keeps one current everywhere, while parallel splits the current into two rates that add back together.

Why it matters

Current becomes a visible flow rate rather than a disconnected number.

Control: Battery voltageControl: Load A resistanceControl: Load B resistanceControl: Use parallel branchesGraph: Branch current vs load BEquation

V

Equation

R_{A}

Equation

R_{B}

Challenge mode

Use the same two-load circuit for compact branch targets. The checklist reads the live branch voltage and current instead of a disconnected topology rule.

0/1 solved

TargetCore

2 of 8 checks

Blue branch at full voltage

Starting from Unequal series loads, rewire the setup so Load B keeps the full battery voltage while its branch current stays around 1 A.

Graph-linkedGuided start2 hints

Suggested start

Use the branch-voltage graph and the node guide together while you rewire the blue branch.

Pending

Open the Load voltage vs load B graph.

Branch current vs load B

Matched

Keep the Voltage labels visible.

Pending

Keep the Node guide visible.

Off

Pending

Keep resistance a between 3.8 ohm and 4.2 ohm.

6 ohm

Pending

Keep resistance b between 11.8 ohm and 12.2 ohm.

6 ohm

Pending

Keep branch bvoltage between 11.8 V and 12.2 V.

6 V

Matched

Keep branch bcurrent between 0.95 A and 1.05 A.

1 A

Pending

Keep total current between 3.9 A and 4.1 A.

1 A

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 load A = 6 ohm and load B = 6 ohm in series mode. The equivalent resistance is 12 ohm, so the total current is 1 A. Series keeps the same current through both loads, so resistance changes redistribute voltage rather than splitting current. Load A has 6 V and 1 A, while Load B has 6 V and 1 A. Both loads are dissipating nearly the same power right now.

Equation detailsDeeper interpretation, notes, and worked variable context.

Series equivalent resistance

One series loop makes the resistances add directly.

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

R_{A}

Load A resistance 6 ohm

R_{B}

Load B resistance 6 ohm

Parallel equivalent resistance

Two parallel branches lower the one-number load seen by the battery.

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

R_{A}

Load A resistance 6 ohm

R_{B}

Load B resistance 6 ohm

Whole-circuit Ohm's law

Battery current depends on the battery voltage and the equivalent resistance of the full arrangement.

I_{total} = \frac{V}{R _{eq}}

V

Battery voltage 12 V

Same current in series

A steady series loop carries one current everywhere.

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

Current split in parallel

Branch currents add back together at the junction.

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

Load voltage relation

Voltage across one load depends on the current through that load and the load resistance.

V_{load} = I R

R_{A}

Load A resistance 6 ohm

R_{B}

Load B resistance 6 ohm

Load power

Power sets the rate of energy transfer and explains relative brightness in this bounded model.

P = I V

V

Battery voltage 12 V

R_{A}

Load A resistance 6 ohm

R_{B}

Load B resistance 6 ohm

Charge passed

At one fixed current, the amount of charge that crosses a branch grows linearly with time.

Q = I 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 5 of 60 / 6 complete

Electricity

Earlier steps still set up Series and Parallel Circuits.

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

Previous step: Power and Energy in Circuits.

Start from track beginning

Short explanation

What the system is doing

Series and parallel circuits use the same battery and the same loads, but the path structure is different. One series loop forces the same current through every load, while parallel branches let current split into separate paths and recombine later.

This module stays intentionally bounded to two loads and one topology toggle. That is enough to make current, voltage, brightness, and charge flow feel like one connected story without turning the page into a circuit-design tool.

Key ideas

01In series, the same current crosses both loads, so the battery voltage must be shared between them.

02In parallel, each branch spans the same two nodes, so both loads keep the full battery voltage while the branch currents depend on branch resistance.

03Brightness in this bounded model follows power. Equal bulbs are dimmer in series and brighter in parallel because the power in each load changes when the arrangement changes.

Live branch checks

Solve the exact state on screen.

Use the exact arrangement, resistances, and inspected time on screen. The same live circuit drives the loads, counters, overlays, and graphs below.

Live valuesFollowing current parameters

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

V

Battery voltage

12 V

R_{A}

Load A resistance

6 ohm

R_{B}

Load B resistance

6 ohm

1. Start from the live arrangement

This setup uses series loop, so

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

2. Substitute the current load values

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 adds the two loads into one path, so the equivalent resistance rises and the same loop current must pass through both loads.

Bulb-behavior checkpoint

Two identical bulbs are connected to the same battery. Why do they both look dimmer in series than in parallel even though the battery has not changed?

Prediction prompt

Predict whether each bulb gets less current, less voltage, or both before you switch the equal pair between the two arrangements.

Check your reasoning

In series, the same battery voltage has to be shared across the two bulbs, so the loop current is smaller and each bulb gets less power. In parallel, each bulb keeps the full battery voltage and therefore dissipates more power.

Brightness in this bounded model follows power. Series raises the equivalent resistance and lowers the loop current, while parallel lowers the equivalent resistance and lets each branch keep the full battery voltage.

Common misconception

Parallel makes bulbs brighter because the battery sends more voltage into each branch.

The battery voltage does not get stronger when the topology changes. In parallel, each branch simply keeps the full battery voltage because both branches connect across the same two nodes.

What really changes is the equivalent resistance seen by the battery. Lower equivalent resistance lets the same battery drive a larger total current.

Quick test

Compare cases

Question 1 of 5

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

Two identical loads are connected to the same battery. Which statement best compares the equal series pair with the equal parallel pair?

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 bulb-like loads that can appear either in one series loop or in two parallel branches. A readout card on the right reports the live battery voltage, both load resistances, equivalent resistance, total current, branch currents, branch voltages, and branch powers.

Moving charge markers travel around the actual circuit path, and optional overlays add current arrows, voltage labels, shared-node markers, charge counters, and power badges that explain brightness. Compare mode adds a dashed ghost circuit for the second setup so arrangement changes stay visible on the same stage.

The page is intentionally bounded to one battery and two loads. There is no free-form circuit editor, so every displayed change stays tied to the same beginner-friendly current, voltage, branch, and power logic.

Graph summary

All three response graphs sweep only load B resistance while keeping the battery, load A, and arrangement fixed. The branch-current graph shows total current together with the two load currents, the branch-voltage graph shows how the two load voltages behave, and the load-power graph shows the live brightness logic for both loads.

The time rail still inspects the same stage honestly while the response graphs stay parameter-based. Pausing or scrubbing lets the learner compare charge counters and moving packets at one chosen time without changing the underlying graph sweep.

Keep the circuit path 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.

Reduce the mixed circuitElectricity

Series and Parallel Circuits

See each variable before you move it.

Current flow

Blue branch at full voltage

Electricity

What the system is doing

Solve the exact state on screen.

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

Two identical loads are connected to the same battery. Which statement best compares the equal series pair with the equal parallel pair?

Keep moving through the concept map.

Equivalent Resistance

Power and Energy in Circuits

Basic Circuits