Physics · Circuits

Series and Parallel Circuits

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What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Kirchhoff Loop and Junction RulesWrite the branch equations

Key takeaway

Series circuits have one path, so the same current passes through every load.
Series loads share the source voltage, and the larger resistance takes the larger drop when the current is common.
Parallel branches connect across the same two nodes, so each branch keeps the full battery voltage.
Parallel branch currents depend on branch resistance and add back together at the source.
Bulb brightness follows power, so topology can change brightness even when the battery and loads are unchanged.

Common misconception

Do not say current is used up by the first load or that the battery sends extra voltage into a parallel branch. Track the path structure first, then current, voltage, and power follow.

The battery voltage does not get stronger when you switch to parallel. Each branch keeps the same battery voltage because both branches connect across the same two nodes.

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Write the branch equationsCircuits

Kirchhoff Loop and Junction Rules

Use one small circuit to see the two Kirchhoff habits: currents balance at a split, and voltage rises and drops balance around every closed path.

Reduce the mixed circuitCircuits

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.

Next in Time response with storageCircuits

RC Charging and Discharging

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Equation snapshotSeries equivalent resistance · Parallel equivalent resistanceShow 3 equations

Choose the topology first, find the equivalent resistance the battery sees, then use Ohm's law to connect that one-number load to total current before reading branch voltage and power.

Series equivalent resistance
$R_{eq} = R_{A} + R_{B}$
One series loop makes the resistances add directly.
Parallel equivalent resistance
$R_{eq} = \frac{R _{A} R _{B}}{R _{A} + R _{B}}$
Two parallel branches lower the one-number load seen by the battery.
Whole-circuit Ohm's law
$I_{total} = \frac{V}{R _{eq}}$
Battery current depends on the battery voltage and the equivalent resistance of the full arrangement.

Worked examples

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Frozen walkthrough

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Frozen walkthrough

Use the exact arrangement, resistances, and inspected time shown on screen. The same live circuit drives the loads, counters, overlays, and graphs below, so every calculation matches the stage.

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Example 1 of 2

Frozen valuesUsing frozen 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. Choose the equivalent-resistance rule for the live arrangement

This setup uses series loop, so

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

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

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Step 5 of 6

Electricity

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

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