lecture10 - Physics 2102 Capacitors Physics 2102 Gabriela...

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Unformatted text preview: Physics 2102 Capacitors Physics 2102 Gabriela González Summary (last class) • Any two charged conductors form a capacitor. • Capacitance : C= Q/V • Simple Capacitors: Parallel plates : C = ε 0 A/d Spherical : C = ε 0 4 π ab/(b-a) Cylindrical : C = ε 0 2 π L/ln(b/a) Energy Stored in a Capacitor • Start out with uncharged capacitor • Transfer small amount of charge dq from one plate to the other until charge on each plate has magnitude Q • How much work was needed? dq ∫ = Q Vdq U ∫ = = Q C Q dq C q 2 2 2 2 CV = Energy Stored in Electric Field • Energy stored in capacitor:U = Q2/(2C) = CV2/2 • View the energy as stored in ELECTRIC FIELD • For example, parallel plate capacitor: Energy DENSITY = energy/volume = u = = = CAd Q U 2 2 = Ad d A Q 2 2 ε 2 2 2 A Q ε 2 2 2 2 E A Q ε ε ε = = volume = Ad General expression for any region with vacuum (or air) Dielectric Constant • If the space between capacitor plates is filled by a dielectric, the capacitance INCREASES by a factor κ • This is a useful, working definition for dielectric constant. • Typical values of κ : 10 - 200 +Q- Q DIELECTRIC C = κε0 A/d Example • Capacitor has charge Q, voltage V • Battery remains connected while dielectric slab is inserted. • Do the following increase, decrease or stay the same: – Potential difference? – Capacitance? – Charge? – Electric field? dielectric slab Example (soln) • Initial values: capacitance = C ; charge = Q ; potential difference = V ; electric field = E ; • Battery remains connected • V is FIXED; Vnew = V ( same ) • Cnew = κ C ( increases...
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This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.

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lecture10 - Physics 2102 Capacitors Physics 2102 Gabriela...

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