Example 1 Physical Sizes of Capacitors
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1 apacitance (R. Bolton - 0) apacitance Physics, 7th Edition, utnell & Johnson hapter 9.5, 0. Pages , (R. Bolton - 0) apacitance Example Physical Sizes of apacitors The value of capacitance is proportional to the area and inversely proportional to the spacing between the plates of the capacitor. What is the physical size of a parallel plate capacitor of value arad, if dmm? What is the physical size of a parallel plate capacitor of value μ, if dμm? What is the physical size of a parallel plate capacitor of value 50 f, if d0.μm? (R. Bolton - 0) apacitance and Magnetism
2 apacitance (R. Bolton - 0) Example Solution: (0.6km,0.34m, 3.8um ) a) ε 0 A d 3 d x0 m 6 A.9x0 m 0.63km per side ε 8.854x0 / m 0 Note: Area of Saskatoon is 44km(km per side). b) c) 6 6 d x0 m x0 A 0.3m 0.34m per side ε 8.854x0 / m 0 d A ε x0 m 50x0 5.65x x0 / m m 3.8μm per side 50f is approximately value of RAM memory capacitance. It stores about x0 6 electrons. Dust: x0 7 electrons. (R. Bolton - 0) apacitance 3 Example Dielectric Effects A 5μ capacitor is charged to 5V. It has a dielectric with relative permittivity ε r 45 between its parallel plates. What happens if the dielectric is removed? (R. Bolton - 0) apacitance 4 and Magnetism
3 apacitance (R. Bolton - 0) Example Solution: (V5.3V) Watch out for reused symbols (i.e., ) Q V 5x0 6 5V.5x0 Note that Q Q after. Why?? ε d A after 5 ε aftera d Substituting and rearranging: after 45 ε 45ε 0 5μ.x ε ε after 0 5.5x0 5. V 7.x0 (R. Bolton - 0) apacitance 5 V Q after after 3 after Example 3 Breakdown Voltages alculate the breakdown voltages (i.e., maximum voltages) for each of the following capacitors? Paper (wax): d00μm? Air: Mica Tantalum: dμm? dμm? d0.μm? (R. Bolton - 0) apacitance 6 and Magnetism 3
4 apacitance (R. Bolton - 0) Example 3 Solution: (500V, 3V, 00V, 40V) Paper (wax): 50V/μm 00μm5000V Air: 3V/μm μm3v Mica 00V/μm μm00v Tantalum: 400V/μm 0.μm40V (R. Bolton - 0) apacitance 7 Example 4 ircuit apacitance What is the equivalent capacitance of the following circuit? (R. Bolton - 0) apacitance 8 and Magnetism 4
5 apacitance (R. Bolton - 0) Example 4 Solution: (.5μ) and 3 and 4 are in parallel: + + 0μ + 0μ + 0μ and 6 are in parallel: + 5μ + 5μ , 34, 56, and 7 are in series: total total μ (R. Bolton - 0) apacitance 9 Example 5 Switch losure onsider the circuit shown below. (R. Bolton - 0) apacitance 0 and Magnetism 5
6 apacitance (R. Bolton - 0) The 500n capacitor initially has 3x0-8 of charge on it. The μ capacitor is initially uncharged The switch is open. What happens after the switch is closed? (R. Bolton - 0) apacitance Example 5 Solution: (0.6x0-8,.4x0-8 ) After switch closure, are the capacitors in parallel? Yes. V V V V Q Q V Since charge is conserved Q + 0 Q Q rom above (and substituting for Q) Q Q Q Q 0 Q > (R. Bolton - 0) apacitance and Magnetism 6
7 apacitance (R. Bolton - 0) Rearranging μ Q Q0 3.0x0.4x n + μ 500n Q Q0 3.0x0 0.6x n + μ Note: V00.06V. 0 06V After switch is closed VV0.0V. (R. Bolton - 0) apacitance 3 Example 6 Energy Storage onsider the circuit shown below (from Example #5). (R. Bolton - 0) apacitance 4 and Magnetism 7
8 apacitance (R. Bolton - 0) The 500n capacitor initially has 3x0-8 of charge on it. The μ capacitor is initially uncharged. The switch is open. What is the energy stored on the capacitors and after the switch is closed? (R. Bolton - 0) apacitance 5 Example 6 Solution: (0.90x0-9 J, 0.8x0-9 J) Recall the results from Example 5 (after the switch is closed): 500n μ Now Q W QV Before: W Q Q 0.6x0 Q.4x0 ( 3x0 ) x0 J 500x0 9 V 0.0V V 0.0V (R. Bolton - 0) apacitance 6 and Magnetism 8
9 apacitance (R. Bolton - 0) After: ( 0.6x0 ) (.4x0 ) + 0.8x J Q Q 9 W after x0 x0 Where did the rest of the energy go?? Work done to move charge Heating wire Electromagnetic radiation (R. Bolton - 0) apacitance 7 Example 7 Supplementary (MT II 008) (R. Bolton - 0) apacitance 8 and Magnetism 9
10 apacitance (R. Bolton - 0) (R. Bolton - 0) apacitance 9 (R. Bolton - 0) apacitance 0 and Magnetism 0
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