19.1 Capacitors and capacitance

Capacitance C is the charge stored per volt: C=Q/V. It depends on geometry and dielectric, not on Q and V separately for a fixed capacitor.

For an isolated spherical conductor capacitance depends on radius; for parallel plates it depends on area, separation and dielectric.

A larger isolated sphere has greater capacitance because more charge can be stored for the same potential.

Capacitance is not the same as capacity in coulombs and is not automatically increased by raising voltage.

For a fixed capacitor, Q=CV. The slope of a Q–V graph is C.

Use farads, coulombs and volts; identify whether voltage is across the capacitor and account for dielectric or geometry changes before treating C as constant.

A 220 μF capacitor charged to 5.0 V stores 1.1×10⁻³ C.

The capacitor does not store a fixed amount of charge independent of voltage; C is the proportionality constant.

For capacitors in parallel, C_total=ΣC because voltage is common; in series, 1/C_total=Σ(1/C) because charge magnitude is common on each capacitor.

Draw the topology first and check bounds: parallel capacitance exceeds the largest branch; series capacitance is below the smallest.

Two equal capacitors C in parallel give 2C, while in series they give C/2.

Capacitors do not follow resistor combination rules automatically; the conserved/shared quantity is different.

For parallel capacitors C_total=ΣC; for series 1/C_total=Σ(1/C). Parallel capacitors share voltage, while series capacitors carry equal charge magnitude.

Draw the topology first and check limits: series C is below the smallest, parallel C above the largest.

Two equal 10 μF capacitors give 20 μF in parallel and 5 μF in series.

Capacitor combination rules differ from resistor rules because the shared/conserved quantity is different.