SCIENCE · INVESTIGATE AND EXPLAIN

Derive capacitor combinations from charge and voltage

Capacitor combination rules follow charge and potential constraints, not a memorized resemblance to resistor rules. Parallel capacitors share the same two nodes and voltage. Their source-separated charges add, giving Ceq=C₁+C₂. The equivalent capacitance is larger than either individual capacitance.

Learning outcome: Compare series and parallel at C₂=30 µF, recording charge, voltage and energy ledgers. Change C₂ to 10 µF and check whether the series equivalent remains below the smaller capacitance.

Starting recap

Distinguish charge flow from energy transfer. Identify nodes, choose consistent current/voltage signs and state source and initial conditions before applying algebra.

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Try

For C₁=20 µF, C₂=30 µF in series across 6 V, Ceq=12 µF and common charge=72 µC. Voltages are 3.6 and 2.4 V and total energy is 216 µJ. In parallel, Ceq=50 µF, charges are 120 and 180 µC and total energy is 900 µJ.

Open the experiment

Predict

Will the smaller capacitor have the larger charge or the larger voltage in the initially uncharged series case?

Your prediction and reason

Experiment

Compare series and parallel at C₂=30 µF, recording charge, voltage and energy ledgers. Change C₂ to 10 µF and check whether the series equivalent remains below the smaller capacitance.

Infer capacitor combinations from charge and potential constraints

Worked teaching model · synthetic values · Initially uncharged ideal C1=20 µF and selected C2 connected to an ideal 6 V source until steady state. In series the isolated middle conductor starts neutral; in parallel both capacitors span the same nodes. Ideal dielectric, no leakage. Virtual only.

Second capacitor: 30 µF Connection: 0=series, 1=parallel: 0 choice

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Circuit connections: 6 V source across C1—neutral isolated middle node—C2 in series.

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Calculated evidence ledger — synthetic teaching model
Quantity	Value	Unit
Equivalent capacitance	12	µF
Source separated charge	72	µC
C1 plate-charge magnitude	72	µC
C2 plate-charge magnitude	72	µC
C1 voltage	3.6	V
C2 voltage	2.4	V
Total stored energy	216	µJ

Accessible plot coordinates

Primary plotted points
source voltage (V)	source separated charge (µC)
0	0
1	12
2	24
3	36
4	48
5	60
6	72

Series capacitors share charge magnitude when the initially neutral middle conductor remains isolated.

At the final DC steady state ideal capacitors carry no sustained conduction current. Series capacitor rules are reciprocal to series resistor rules. The total energy equals ½CeqV²; charges are not added across the series pair to infer source charge.

Series capacitors share charge magnitude when the initially neutral middle conductor remains isolated.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Establish the model and evidence

For two initially uncharged capacitors connected in series, the isolated middle conductor remains net neutral. Its two facing plates therefore acquire equal opposite charges, giving the same charge magnitude on each capacitor. Their voltages add to the source voltage, so 1/Ceq=1/C₁+1/C₂. The smaller capacitor has the larger voltage for that common charge. An initially charged middle node would require a different charge account.

The phrase “charge stored” means the magnitude separated on a capacitor, not net charge created. Adding the two series plate-charge magnitudes to infer the source-separated charge double counts the same transfer constraint. In parallel, by contrast, the source supplies separate branches and those charges do add. Always identify the source terminals and the middle-node boundary.

At the final DC steady state, ideal capacitors maintain voltage while sustained conduction current through their branches is zero. During charging the wires carry transient current even though charges do not cross the insulating dielectric. Total stored energy must agree both with the sum of ½CiVi² and with ½CeqVsource² for the stated initial conditions. This browser task does not involve handling real charged capacitors.

Worked evidence

Predict and investigate

Will the smaller capacitor have the larger charge or the larger voltage in the initially uncharged series case?

Compare series and parallel at C₂=30 µF, recording charge, voltage and energy ledgers. Change C₂ to 10 µF and check whether the series equivalent remains below the smaller capacitance.

Transfer to changed conditions

Find equivalent capacitance, individual voltages and common charge for 12 and 24 µF initially uncharged capacitors in series across 9 V.

Compare the worked transfer

Ceq=8 µF and common Q=72 µC. The voltages are 6 V across 12 µF and 3 V across 24 µF. Their sum is 9 V, and energy is 324 µJ.

Explain the boundary

Which initial-condition assumption justifies equal series charge, and why is it not a statement that current crosses the dielectric?

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original cases and computed/synthetic evidence, not actual laboratory measurements. These activities are virtual only: do not reproduce wiring, short-circuit, battery charging, heating or charged-capacitor experiments. Any real practical work requires qualified supervision and an independently approved safety procedure.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Which initial-condition assumption justifies equal series charge, and why is it not a statement that current crosses the dielectric?

Your explanation and limitations

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Previous: Interpret negative loop current and source absorption Next: Infer an RC time scale without confusing energy and charge

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