PHYS 221 Recitation Kevin Ralphs Week 3

Overview HW Questions Capacitance Capacitors Dielectrics

HW Questions Ask Away….

Capacitance 𝑄=𝐶∆𝑉 What does it tell me? Why do I care? The charge that accumulates on two conductors is proportional to the voltage between them 𝑄=𝐶∆𝑉 Q: charge on the capacitor’s plates, C: capacitance, ΔV: potential difference across the capacitor Why do I care? Capacitors are vital components in electronics They can be used to temporarily store charge and energy, and play an even more important role when we move to alternating current systems Camera flashes, touch screen devices, modern keyboards all exploit capacitance

Capacitance What does capacitance depend on? Geometry of the plates Material between the plates For parallel plates: 𝐶= 𝜀𝐴 𝑑 C: capacitance, ε: permittivity of the material between the plates, A: area of the plates (may or may not be square), d: distance between the plates Unit of capacitance is the Farad To demystify this, units are (meters*permittivity)

Capacitance The permittivity of free space has no physical meaning It merely changes physical quantities into their appropriate SI units Physical Units SI Units Length Farads Length/Charge Volts Length^2/Charge^2 Newtons Length/Charge^2 Joules

Capacitance Dielectric Put simply, a dielectric is a material (an insulator) that in all, but very rare cases weakens the electric field around it This allows more charge to be placed on the plates for the same voltage (i.e. capacitance is increased) The permittivity of a dielectric tells you how it affects the capacitance The ratio of the permittivity of a dielectric and the permittivity of free space is the dielectric constant 𝜅= 𝜀 𝜀 𝑜 = 𝐶 𝑑 𝐶 𝑣𝑎𝑐 κ: dielectric constant, ε: permittivity of a material, εo : permittivity of free space, Cd : capacitance with a dielectric, Cvac: capacitance in the vacuum

Capacitance A charged capacitor has potential energy 𝑈= 𝑄 2 2𝐶 = 1 2 𝐶( ∆𝑉) 2 = 1 2 𝑄∆𝑉 U: stored potential energy, Q: charge on the capacitor, C: capacitor’s capacitance, ΔV: voltage across the capacitor

Capacitance In circuits In well-behaved configurations, capacitors may be combined into a single equivalent capacitor Parallel 𝐶 𝑒𝑞 = 𝐶 𝑖 * This is like increasing the area of the plates * Series 𝐶 𝑒𝑞 = 1 𝐶 𝑖 −1 * This is like increasing the separation distance *

Capacitance Capacitors are in equilibrium Series: when they have the same charge Parallel: when they have the same voltage