Physics · Electricity

Capacitance and Stored Electric Energy

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Wrap-up

What you learned

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Read next: RC Charging and DischargingTurn stored charge into a time response.

Key takeaway

Plate area and plate separation set capacitance before the battery voltage is applied.
At fixed voltage, a larger capacitance stores more charge and more electric energy.
For fixed geometry, stored charge grows linearly with voltage while stored energy grows with voltage squared.
The same battery voltage can lead to different stored charge when the capacitor geometry changes.

Common misconception

Do not treat voltage as the whole capacitor story. Geometry sets C first, and the battery then turns that capacitance into Q and U.

Voltage alone does not determine storage. Geometry still sets the capacitance first.

Carry stored charge into circuits

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Turn storage into time responseCircuits

RC Charging and Discharging

Keep one resistor-capacitor loop on screen so capacitor voltage, current, stored energy, and the time constant all stay tied to the same charging or discharging setup.

Carry stored charge into a live loopCircuits

Basic Circuits

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.

Connect storage to power and energyCircuits

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.

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Reference and support

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Equation snapshotParallel-plate capacitance · Stored chargeShow 3 equations

Read C = A / d as the geometry rule first; then use Q = CV and U = 1/2 C V^2 to turn that capacitance into charge and energy.

Parallel-plate capacitance
$C = v a r e p s i l o n df r a c A d$
Capacitance grows with facing area and shrinks with separation.
Stored charge
$Q = C V$
At fixed voltage, a larger capacitance stores more opposite charge on the plates.
Stored electric energy
$U = t f r a c 12 C V^{2} = t f r a c 12 Q V$
Stored energy depends on geometry through C and grows quadratically with voltage.

Why it behaves this way

Explanation

Capacitance tells you how much charge a capacitor stores for each volt across it. This bench keeps one battery attached to one bounded pair of parallel plates so geometry, stored charge, field strength, and stored electric energy stay tied to the same setup.

The capacitor story stays geometric first. Plate area and plate separation set the capacitance, then the battery voltage determines how much charge builds on the plates and how much electric energy is stored in the field between them.

Key ideas

01For this bounded model with epsilon = 1 in displayed units, capacitance follows C = A / d.

02At fixed voltage, stored charge follows Q = CV.

03Stored electric energy follows U = 1/2 C V^2, so energy grows faster with voltage than charge does.

Worked examples

Live capacitor checks

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Frozen walkthrough

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Frozen walkthrough

Use the current plate geometry and battery setting directly from the bench.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current plate area and separation, what capacitance does this capacitor have?

A

Plate area

2 area

d

Plate separation

2 m

1. Start from the bounded plate rule

Use

C = A / d

because this bench keeps

v a r e p s i l o n = 1

in the displayed units.

2. Substitute the current geometry

C = 2/2

3. Compute the capacitance

That gives

C = 1

Capacitance

C = 1

This geometry gives a moderate capacitance, so the storage story stays easy to compare against voltage changes.

Quick test

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Accessibility

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The simulation shows one parallel-plate capacitor connected to one battery. Sliders change the effective plate area, the gap between the plates, and the battery voltage while overlays can show the field region, opposite charge building on the plates, the geometry guide, and a stored-energy cue.

The capacitor picture, readout card, and voltage-response graph all update from the same controls so geometry and voltage changes stay tied to one bounded setup.

Graph summary

The voltage-response graph plots stored charge and stored electric energy for the current capacitor geometry as battery voltage changes. The charge curve is linear while the energy curve bends upward because voltage is squared in the energy relation.

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