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# 24 - CAPACITANCE AND DIELECTRICS 24 24.5 IDENTIFY SET UP...

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C APACITANCE AND D IELECTRICS 24.5. I DENTIFY : ab Q C V . 0 A C d P . S ET U P : When the capacitor is connected to the battery, 12.0 V ab V . E XECUTE : (a) 6 4 (10.0 10 F)(12.0 V) 1.20 10 C 120 C ab Q CV (b) When d is doubled C is halved, so Q is halved. 60 C Q . (c) If r is doubled, A increases by a factor of 4. C increases by a factor of 4 and Q increases by a factor of 4. 480 C. Q E VALUATE : When the plates are moved apart, less charge on the plates is required to produce the same potential difference. With the separation of the plates constant, the electric field must remain constant to produce the same potential difference. The electric field depends on the surface charge density, . To produce the same , more charge is required when the area increases. 24.12. I DENTIFY : Apply the results of Example 24.3. / C Q V . S ET U P : 15.0 cm a r . Solve for b r . E XECUTE : (a) For two concentric spherical shells, the capacitance is 1 a b b a r r C k r r . b a a b kCr kCr r r and 12 12 (116 10 F)(0.150 m) 0.175 m (116 10 F) 0.150 m a b a kCr k r kC r k . (b) 220 V V and 12 8 (116 10 F)(220 V) 2.55 10 C Q CV . E VALUATE : A parallel-plate capacitor with 2 4 0.33 m a b A r r and 2 2.5 10 m b a d r r has 0 117 pF A C d P , in excellent agreement with the value of C for the spherical capacitor. 24.14. I DENTIFY : The capacitors between b and c are in parallel. This combination is in series with the 15 pF capacitor. S ET U P : Let 1 15 pF C , 2 9.0 pF C and 3 11 pF C . E XECUTE : (a) For capacitors in parallel, eq 1 2 C C C so 23 2 3 20 pF C C C (b) 1 15 pF C is in series with 23 20 pF C . For capacitors in series, eq 1 2 1 1 1 C C C so 123 1 23 1 1 1 C C C and 1 23 123 1 23 (15 pF)(20 pF) 8.6 pF 15 pF 20 pF C C C C C . E VALUATE : For capacitors in parallel the equivalent capacitance is larger than any of the individual capacitors. For capacitors in series the equivalent capacitance is smaller than any of the individual capacitors.

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24 - CAPACITANCE AND DIELECTRICS 24 24.5 IDENTIFY SET UP...

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