Use one bounded circuit branch to connect current, voltage, Kirchhoff balance, time response, non-ideal source behavior, power, and equivalent resistance without leaving the same battery-and-load language.
Use this topic when you want the circuit story itself, not the earlier charge-field setup. The page starts with one simple loop, then keeps the same battery-and-load language while power and energy, series versus parallel structure, Kirchhoff loop and junction balance, RC charging and discharging, internal resistance, and equivalent resistance make larger circuits readable.
Best first concepts
The topic page keeps these starts in their own compact row so the first screen is about orientation and next action, not stacked feature cards.
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.
Circuits and Ohm's law
Strong first stop for getting into this topic without scanning the whole library.
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.
Series and parallel branches
Strong first stop for getting into this topic without scanning the whole library.
Specific learning goals
These goal cards stay authored and transparent. They reuse the current topic page, starter tracks, guided collections, concept bundles, and progress cues instead of adding a separate recommendation system on top of this branch.
Use the electricity topic route, the authored bridge lesson set, and the main electricity track when the field-to-voltage-to-circuit handoff should stay explicit.
Primary move
Open topic route
No saved progress yet inside Electricity.
Entry diagnostic
Start from the opening step
No saved diagnostic checks are available yet, so the opening step is still the best entry into the collection.
Reuses the guided collection entry for Electricity Bridge Lesson Set, with 0 of 2 probes already ready.
No saved progress yet inside Electricity.
Open the electricity topic route is the next guided collection step.
Electric Fields is the next best step inside Electricity.
No saved progress yet for Electric Potential.
Use the electricity route, the existing electricity-to-magnetism bridge collection, and the magnetic starter track so the transition into electromagnetism stays bounded and transparent.
Primary move
Start Electricity
Electricity is the authored prerequisite for Magnetism. Electric Fields opens this track and sets up the rest of the path. Nothing is hard-gated here; this is simply the authored prep path.
Entry diagnostic
Start from the opening step
No saved diagnostic checks are available yet, so the opening step is still the best entry into the collection.
Reuses the guided collection entry for Electricity to Magnetism Bridge, with 0 of 2 probes already ready.
Recommended prep
Electricity is the authored prep route for Prepare for the electromagnetism branch. Nothing is hard-gated here; this is simply the intended setup path.
No saved progress yet inside Circuits.
Reopen the electricity track in recap mode is the next guided collection step.
Magnetic Fields is the next best step inside Magnetism.
No saved progress yet for Maxwell's Equations Synthesis.
Grouped concept overview
Each group is authored in the topic catalog, but the actual concepts, progress badges, and track cues still come from the canonical concept metadata and shared progress model.
Group 01
Start with the simplest closed path, then keep the same circuit language while power and accumulated energy become measurable.
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.
Strong first stop for getting into this topic without scanning the whole library.
Keep one source and one resistive load in view while current, power, and accumulated energy over time stay tied to the same honest circuit.
Group 02
Then compare how current and voltage behave across branches, write the loop and junction equations that balance them, and only then reduce the network to an equivalent resistance.
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.
Strong first stop for getting into this topic without scanning the whole library.
Write one current-balance equation at a junction and one voltage-balance equation around a loop on the same bounded grouped circuit, then see those equations match the live branch currents and drops.
Reduce one highlighted resistor group into an equivalent block, then collapse the whole mixed circuit honestly and watch how the total current and grouped behavior change together.
Group 03
Close the branch with one resistor-capacitor loop so charging, discharging, and tau = RC connect capacitor storage to circuit timing.
Group 04
Finish by giving the source an internal resistance so emf, terminal voltage, and wasted power stay in one honest one-loop model.