f Facebook cowww.webassi x Chapter 27 Homework x Pairs a p ralle wires Dr co211

Question

f Facebook cowww.webassi x Chapter 27 Homework x Pairs a p ralle wires Dr co211 cables re two conduc ors spiarat d by an insulator, so they haver, capacitance For a given cable, he c pacitance s Independent a th ength it the cable ts very ong. A typica arcuit mode a shown in the figure below. It is called a lumped-parameter model and represents how a unit length ef the cable behaves. Find the equivalent capacitance of the following lengths. (Use the following as necessary: C.) table Ci C A. One unit length B. Two unit lengths C. Infinite number of unit lengths (a) ane unit length (Figurr A) (b) two unit lengths (Figure B) () an infinite number of unit lorgths (Figurc C). Hint: For the infinitc number of units, adding one more unit at the bcginning docs not change the cquivalent capocitoncc. Need Help? Read It o -1 points KazPSE'1 27 RG8. My Notes Ask Your A parallel plate capactor nas square plates of s de 5 2.80 cm and plate separ tion d 2.60 mm. The capacit 5 charged by battery to charge Q (x 65) is then ir sertr distance y-1.00 rm into the capacitor see figure below). Hint: Consider the system as two capacitors connected In parallel 4.30 pC, after which the battey is disconnected. A porcelain d'electric 10034 PM Type: here to search

Explanation / Answer

part a )

capacitor are in series combination

in series 1/Ceq = 1/C1+1/C2+1/C3

Ceq = C/2

part b )

right most capacitor and upper branch right side capacitor in parallel

C' = C/2  

middle one in parallel with C"= C'+C = 3C/2

C" in series with C

Ceq = 3C/5

part c )

first we find a unit cell after that repetation is starting

After removing that unit which is equal to Ceq and total capacitance of circuit is also Ceq

now Ceq in parallel with C and their equivalent in series with C  

Ceq = C*(C+Ceq)/[C+(C+Ceq)]

Ceq = C^2 + Ceq / [ 2C + Ceq]

Ceq^2 + C*Ceq - C^2 = 0

by solving this quadratic equation

Ceq = C*(sqrt(5)-1)/2

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