303L-HW12

303L-HW12 - fierro (jmf2547) – HW12 – berk – (60290)...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: fierro (jmf2547) – HW12 – berk – (60290) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A capacitor network with air-filled capacitors as shown below. 37 . 7 V 75 . 5 μ F 75 . 5 μ F 75 . 5 μ F 75 . 5 μ F b a c d When the top right-hand capacitor is filled with a material of dielectric constant κ , the charge on this capacitor is increases by a fac- tor of 1 . 46. Find the dielectric constant κ of the mate- rial inserted into the top right-hand capaci- tor. Correct answer: 2 . 7037. Explanation: Let : C 1 = C = 75 . 5 μ F , C 2 = C = 75 . 5 μ F , C 3 = C = 75 . 5 μ F , C 4 = C = 75 . 5 μ F , E B = 37 . 7 V , and Q ′ = 1 . 5 Q . E B C 1 C 3 C 2 C 4 b a c d The capacitors C 3 and C 4 have nothing to do with this problems. In addition, the capac- itances are all equal and their specific values are immaterial. Furthermore, the electric po- tential of the battery is not required. C 1 = C 2 = C 3 = C 4 , where Q and Q ′ are the initial and final charges on C 2 and Q ′ Q ≡ α =ratio of final to initial charge on C 2 . We know the charges on C 1 and C 2 are the same. Initially, V ab = V 1 + V 2 = Q C 1 + Q C 2 = Q C + Q C = 2 Q C . (1) Therefore Q = 1 2 V ab C . After the dielectric material is inserted in C 2 , the capacitance becomes C ′ 2 = κ C . There- fore, V ab = V ′ 1 + V ′ 2 = Q ′ C 1 + Q ′ C ′ 2 = Q ′ C + Q ′ κ C = κ + 1 κ Q ′ C , and using Eq. (1) and solving for Q ′ , we have 2 Q C = κ + 1 κ Q ′ C Q ′ = κ κ + 1 V ab C = κ κ + 1 2 Q Q ′ Q ≡ α = 2 κ κ + 1 = 1 . 46 . Solving for κ , we have κ = α 2- α = 1 . 46 2- 1 . 46 = 2 . 7037 . 002 10.0 points Consider the two cases shown below. In Case fierro (jmf2547) – HW12 – berk – (60290) 2 One two identical capacitors are connected to a battery with emf V . In Case Two, a di- electric slab with dielectric constant κ fills the gap of capacitor C 2 . Let C 12 be the resultant capacitance for Case One and C ′ 12 the resul- tant capacitance for Case Two. Case One V C 1 C 2 Case Two V C 1 C ′ 2 κ The ratio C ′ 12 C 12 of the resultant capacitances is 1. C ′ 12 C 12 = κ . 2. C ′ 12 C 12 = 2 κ. 3. C ′ 12 C 12 = 1 + κ ....
View Full Document

This document was uploaded on 10/10/2008.

Page1 / 7

303L-HW12 - fierro (jmf2547) – HW12 – berk – (60290)...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online