{Part a} A 1.92-nF parallel-plate capacitor is charged to an initial potential d
ID: 1280098 • Letter: #
Question
{Part a}
A 1.92-nF parallel-plate capacitor is charged to an initial potential difference ?Vi = 100 V and is then isolated. The dielectric material between the plates is mica, with a dielectric constant of 5.
a.)How much work is required to withdraw the mica sheet?
{Part b}
Suppose you wish to fabricate a uniform wire from a mass m of a metal with density ?m and resistivity ?. If the wire is to have a resistance of R and all the metal is to be used, what must be the length and the diameter of this wire? (Use any variable or symbol stated above as necessary to creat formula.)
a.) I = __
b.) d =__
Explanation / Answer
Q = C V = 1.92 * 10-9 * 100 = 1.92 * 10-7 C
W = U2 - U1 = Q2/C
= 1.92 * 10-7 * 1.92 * 10-7 * (1/(1.92 * 10-9/5) - 1/1.92 * 10-9)
W = 7.68 * 10-5 J
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p m = m / V
m = pm * V = (pm) * A * l
A = m / (pm) * l
R = p * l / A
R = (p * l) / (m /(pm)*l) = (p * (pm) * l2 ) / m
l = sqrt [ R m / p * pm ]
V = m / (pm)
pi * r2 * l = m / (pm)
r = 1/2 d
pi * (1/2 d )2 * l = m/(pm)
pi * (1/2 d )2 * [sqrt(m*R / p*(pm))] = m/(pm)
d = 2 * [ sqrt ( m/pm*pi) ] * [sqrt( m * R / p * pm)]
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