Solution 11 - homework 11 KANUNGO ANIL Due 4:00 am For a...

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homework 11 – KANUNGO, ANIL – Due: Sep 29 2007, 4:00 am 1 Question 1, chap 26, sect 3. part 1 of 1 10 points A capacitor is constructed from two metal plates. The bottom portion is filled with air and the top portion is filled with material of dielectric constant κ . The plate area in the top region is the same as that in the bottom region. Neglect edge effects. κ E Determine the ratio U t U b of energy stored in the top portion to the bottom portion. 1. U t U b = κ + 1 2. U t U b = κ correct 3. U t U b = κ 2 4. U t U b = 1 κ 5. U t U b = 1 κ 2 6. U t U b = 2 κ + 1 7. U t U b = 1 2 κ 8. U t U b = 1 κ + 1 9. U t U b = 1 2 κ + 1 10. U t U b = 2 κ Explanation: For a capacitor with dielectric κ , C = κǫ 0 A d Energy stored in a charged capacitor: U = 1 2 Q V = 1 2 V 2 C = 1 2 Q 2 C . C t C b The capacitance of a capacitor is deter- mined solely by the dielectric constant of the material and geometric configuration of the capacitor. The bottom portion and the top portion may be treated as two capacitors connected in parallel. Here V b = V t = V . Therefore, U t U b = 1 2 V 2 C t 1 2 V 2 C b = C t C b = κ . Question 2, chap 26, sect 3. part 1 of 2 10 points A capacitor is constructed from two square metal plates. The gap between the plates is filled with two dielectrics of equal size as shown in the figure below. Neglect edge ef- fects. 1 . 31 cm 0 . 97 mm dielectric constant right 9 . 7 dielectric constant left 2 . 74 Calculate the capacitance C of the device.
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homework 11 – KANUNGO, ANIL – Due: Sep 29 2007, 4:00 am 2 Correct answer: 6 . 69347 pF (tolerance ± 1 %). Explanation: Let : L = 1 . 31 cm = 0 . 0131 m , d = 0 . 97 mm = 0 . 00097 m , κ = 2 . 74 , κ r = 9 . 7 , and ǫ 0 = 8 . 85419 × 10 12 F / m .
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