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Concept module

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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Starter track

Step 6 of 60 / 6 complete

Electricity

Earlier steps still set up Equivalent Resistance.

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

Previous step: Series and Parallel Circuits.

Start from track beginning

Why it behaves this way

Explanation

Equivalent resistance lets you replace a bounded group of resistors with one simpler block that draws the same total current from the same source. The reduction is only honest when the grouped resistors really share one series path or the same two nodes.

This module stays intentionally small. One outer resistor always sits in series with a highlighted two-resistor group, and that group can switch between series and parallel. That is enough to teach reduction order, grouped voltage and current behavior, and the effect on the total circuit without turning the page into a symbolic circuit solver.

Key ideas

01Reduce the highlighted group first, then combine that one-number result with the outer resistor that stays in series with the whole block.

02When the grouped pair is in series, the same current crosses both grouped resistors before you add their resistances. When the grouped pair is in parallel, both grouped branches share the same group voltage before you combine them.

03A smaller total equivalent resistance lets the same battery drive a larger total current, so the reduction step is not bookkeeping only. It changes the live circuit behavior everywhere.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the exact circuit on screen. The same resistor values, group mode, inspected time, overlays, and response graphs drive the reduction steps below.

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Frozen valuesUsing frozen parameters

For the current circuit, what equivalent resistance does the highlighted pair reduce to, what total equivalent resistance does the source feel, and what total current follows?

V

Battery voltage

12 V

R_{1}

Outer resistor

4 ohm

R_{2}

Grouped resistor 2

6 ohm

R_{3}

Grouped resistor 3

6 ohm

1. Start from the live grouped pair

The highlighted pair is a series grouped pair, so

R_{group} = R_{2} + R_{3}

2. Reduce the grouped pair numerically

With

R_{2} = 6

and

R_{3} = 6

R_{group} = 6 + 6

, so

R_{group} = 12

3. Add the outer series resistor

Because

R_{1}

stays in series with the whole block,

R_{eq} = 4 + 12

, so

R_{eq} = 16

4. Use the total equivalent in Ohm's law

I_{total} = \frac{V}{R _{eq}} = \frac{1}{2} 16 = 0.75

Grouped and total equivalent resistance

R_{group} = 12, R_{eq} = 16, I_{total} = 0.75

The grouped pair reduces by direct addition first, so the total equivalent stays larger before the source current is found.

Reduction-order checkpoint

The highlighted pair starts as two 6 ohm resistors in series with R1 = 4 ohm and the same 12 V battery. If you switch only the highlighted pair to parallel, why does the total current jump so much?

Make a prediction before you reveal the next step.

Predict whether the big change comes from R1 changing, from the grouped pair changing, or from both before you switch the group mode.

Check your reasoning against the live bench.

The grouped pair changes from 12 ohm in series to 3 ohm in parallel, while R1 stays the same 4 ohm resistor. That drops the total equivalent from 16 ohm to 7 ohm, so the same battery drives a much larger total current.

Equivalent resistance is causal here, not decorative. The live source current follows the one total load that remains after the grouped pair is reduced honestly.

Common misconception

Equivalent resistance is just a shortcut number, so it does not really tell you anything about the current or voltage in the original circuit.

The equivalent resistance is defined by matching the total current drawn from the same source. If the source sees the same voltage and the same total current, the simplified circuit is telling you something physically real about the original one.

What you cannot do is ignore the reduction order. You must first identify a group that truly behaves like one series block or one parallel block before replacing it.

Quick test

Reasoning

Question 1 of 5

Answer from the live grouped circuit, not from detached formulas. Each question asks what the stage, reduction card, or linked graphs must mean.

Which part of the circuit should you reduce first in this module?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows one battery on the left, one outer resistor labeled R1 on the top path, and a highlighted two-resistor group to the right. The highlighted group can appear either as two series resistors on the same path or as two parallel branches between the same two group nodes.

Moving charge markers follow the actual current paths, and optional overlays add current arrows, voltage labels, node markers, charge counters, and a reduction guide that highlights the pair that should be simplified first. A reduction card on the right shows the live grouped equivalent and the final total equivalent before the readout card lists the current grouped state.

Compare mode adds a dashed ghost circuit for the second setup so only the changed grouped relationship needs to be noticed. The page stays intentionally bounded to one outer resistor and one two-resistor group.

Graph summary

All three graphs sweep only R3 while keeping the battery, R1, R2, and the grouped-pair mode fixed. The reduction sweep shows the grouped equivalent together with the final total equivalent, the current graph shows total current alongside the grouped resistor currents, and the voltage-share graph shows how the outer drop, grouped-block drop, and live R3 drop behave as R3 changes.

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

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Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Power consequencesElectricity