Physics · Circuits

Basic Circuits

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Series-Parallel CircuitsExtend the one-loop and two-branch ideas to mixed resistor networks.

Key takeaway

Ohm's law connects battery voltage, equivalent resistance, and total current for the live circuit.
Series resistors share one loop current and split the source voltage across their drops.
Parallel branches each span the full battery voltage while their branch currents add to the total current.
Changing topology can change equivalent resistance even when the battery and resistor values stay the same.

Common misconception

Do not treat current as something that gets used up by each resistor. In a steady series loop the current is the same everywhere; voltage drops tell the energy-per-charge story.

Current is not used up by a resistor. In a steady series loop, the same amount of charge per second passes every point in the loop.

Continue with related ideas

Keep this idea moving

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See rate and total in the same loopCircuits

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.

Compare branch topologiesCircuits

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.

Reduce mixed groupsCircuits

Equivalent Resistance

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.

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Reference and support

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Equation snapshotOhm's law · Series equivalent resistanceShow 3 equations

Start with the topology to find the one-number resistance the battery sees, then use Ohm's law to connect that load to total current.

Ohm's law
$I = \frac{V}{R}$
For one fixed resistance, doubling the voltage doubles the current.
Series equivalent resistance
$R_{eq} = R_{A} + R_{B}$
Two series resistors act like one larger resistor because the same loop current must pass through both.
Parallel equivalent resistance
$R_{eq} = \frac{R _{A} R _{B}}{R _{A} + R _{B}}$
Two parallel branches reduce the total load because charge has multiple paths between the same two nodes.

Worked examples

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Frozen walkthrough

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Frozen walkthrough

Use the values from the circuit now on screen. The same battery, resistor values, and topology determine the stage, readout, overlays, and graphs, so every calculation matches the live setup.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current circuit, what equivalent resistance does the battery see, and what total current follows from it?

V

Battery voltage

12 V

R_{A}

Resistor A

6 ohm

R_{B}

Resistor B

6 ohm

1. Choose the correct equivalent-resistance rule for this topology

This setup uses series loop, so

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

2. Substitute the live resistor values

With

R_{A} = 6

and

R_{B} = 6

R_{eq} = 6 + 6

, so

R_{eq} = 12

3. Apply Ohm's law to the whole circuit

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

4. Calculate 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.

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Starter track

Step 3 of 6

Electricity

Basic Circuits appears later in this track, so it is cleaner to start from the beginning first.

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