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Final

# PCS 211 Final: Chapter 26 Premium

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School
Department
Physics
Course
PCS 211
Professor
Alexandre Douplik
Semester
Winter

Description
▯ ▯ ▯ ▯ Capacitance Use CapacCito26. Capacitance and Dielectrics Unitstfreapsciteaci:srlrotitalntlpyntgtve.nergy. mmF = micromicrofarad = picofarads = 1x10 AC fciter,iterunestereni)lyanfrruice,siteceenge and a r: two conductors having : C ▯Q/V F = 1 ▯ F, -12 F = 1 pF General procedureion of Capacitance StepS3teCSteQa/l.ulcearge of magnitude of Q is assumed. To increase capacitance: increase (2) 1)eAeectiefindpbatehasawchprats:, and other –Q.acitor: The potential difference between two plates: (3) C C = = ▯ V Q d A = V E Qd = = Ed ▯ ▯ ▯ Q 0 = A = ▯ 0▯ Qd A Q A Aor decrease +Q d d Area =A -Q In case of an isolated conducting sphere, assume b)hess(Geuhs’sLarg):is Q and -Q Example: The capacitance of an spherical conductor C = V Q MagnibVde E = C ▯ = e a = aV e = V Q = r2 Q ▯▯ = V ▯ (b > r > a) 0 ek E a b ab k rdr ▯ eQ = ) ( ▯ ab ▯ ek a ▯ (>0)ra dr -Q 2 k eQ b ▯ ▯ ▯ b ▯ a 1 a ▯ (<0) +Q ▯ Example: If C, C Potential difference in a parallel cParallel Combination: of Capacitors Total Capacitance: Q 1 eq eq eq = 2 = C= C = Q ▯ F, C1+ C+ Ctotal /V = (Q V = V 2= 4 2 2 total + C = Q ▯ 1= V F the+ C 1+ Q 1+ Q ••• , 2 2 )/V = Q eq = 6 1 ▯ /V + Q F 2 /V C ExampleGenerally, must be the same on all the plates.ies Combination of Capacitors CapacPotentiadifarence:s ombination, the magnitude of the charge C C eq 1 eq 1 = eq 1= C = V = 4 C 1 Q total C 2= 8 1 + eq F C = = ▯ 2 1 1V V F then + Q + totaQ 3 1 V total +••• =2 = V C Q V eq 1 1 1 = + + V 8 Q 2V ▯ 1 = 2, F C 1 + 1 ▯ 1 + F 2 1 = 4 F 1 26.4 Energy Stored in a Charged Capacitor Define: is stored in the electric field created between the platesork needed to transfer +acitor. The above 3 expressions are totally equivalent. Energy density U U W dW = ▯ = = 2▯1 0A/d into W 0 ▯ Q = 0E = C q Vdq Eu 2 2 Q dq = (Ad) C 2 = = 2 1 U = 2 Q Cdqq 0▯ or = , QV1 C 2 E energy per unit▯volume 2 ene0Ey stored in a c=pacitor dq 2
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