lecture10 - Physics 2102 Capacitors Physics 2102 Gabriela...

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Unformatted text preview: Physics 2102 Capacitors Physics 2102 Gabriela Gonzlez Summary (last class) Any two charged conductors form a capacitor. Capacitance : C= Q/V Simple Capacitors: Parallel plates : C = 0 A/d Spherical : C = 0 4 ab/(b-a) Cylindrical : C = 0 2 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 2 2 2 A Q 2 2 2 2 E A Q = = 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 This is a useful, working definition for dielectric constant. Typical values of : 10 - 200 +Q- Q DIELECTRIC C = 0 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 = C ( increases...
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lecture10 - Physics 2102 Capacitors Physics 2102 Gabriela...

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