Capacitance and Charge

Capacitor as Store

A capacitor-as-store scan holds the capacitance fixed and varies the voltage across three rows, checking that stored charge Q = C * V rises one-for-one with voltage on the same ideal capacitor row by row. The arithmetic is exact only for the stated capacitances, voltages, charges, and rows in the ideal capacitor, lumped-element model. Real capacitors add leakage, dielectric absorption, ESR, voltage-rating limits, plate/fringe geometry, meter/probe calibration limits, finite precision, and measurement uncertainty.

A capacitor stores separated charge. Capacitance tells how much charge appears for each volt. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Read the capacitance

A capacitor is a two-plate device. This one has capacitance 2 farads.

C=2 FC = 2\ \text{F}
Capacitor componentA two-plate capacitor is labelled with its capacitance.2 F

Use schematic farads

A farad is a large capacitance. These clean farad values are schematic training values for exact arithmetic.

clean farads are schematic values\text{clean farads are schematic values}

Connect a voltage

At 6 volts, the capacitor stores separated charge.

V=6 VV = 6\ \text{V}
Capacitor componentA two-plate capacitor is labelled with its capacitance.2 F

Compute stored charge

The stored charge is 12 coulombs.

Q=CV=2 F⋅6 V=12 CQ = C V = 2\ \text{F}\cdot 6\ \text{V} = 12\ \text{C}
Capacitor componentA two-plate capacitor is labelled with its capacitance.2 F

Stored charge rises with voltage

Hold the capacitance at 2 farads. More volts put more separated charge on the same ideal capacitor. The diagram shows the middle row.

CVQ2 F3 V6 C2 F6 V12 C2 F9 V18 C\begin{array}{c|c|c}C&V&Q\\2\ \text{F}&3\ \text{V}&6\ \text{C}\\2\ \text{F}&6\ \text{V}&12\ \text{C}\\2\ \text{F}&9\ \text{V}&18\ \text{C}\\\end{array}
Capacitor componentThe middle table row is the checked diagram.2 F