Problems Unit IV CAPACITORS & DIELECTRICS 1. You are given a paralle1 plate capa
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Problems Unit IV CAPACITORS & DIELECTRICS 1. You are given a paralle1 plate capacitor with square plates of area A and separation d, in a vacuum. What is the qualitative effect of each of the following on its capacitance? a. Reduce d. c. Double the area of both plates. d. Double the potential difference between the plates. d. Dubie s the arcopper betven the plates, touching nei ther plate. e. Tilt one plate so that the separation remains d at one end but is d/2 at the other. 2. A parallel plate capacitor has circular plates of 8 cm radius and 1 mm separation. a. Find its capacitance. (56.6T pF) b. If a 100 V battery is connected across the capacitor, what charge will appear on the plates? (5.7m nC)Explanation / Answer
1. given parallel plate capacitor
plate area = A
seperation = d
medium = vaccum
a. capacitance of parallel plate capacitor is given by
C = A*epsilon/d
hence
reducing d will increase the capacitance
b. when we put a slab of copper inside the paltes and it is not touching any of the plates
inserting a metal slab inside the plates of a capacitor does not change the electric field inside the cpacitor
nor the potential differnce
hence everything remains the same
c. double the area of both plates :
so increasing A will double the capacitanc eof the capacitor as well
d. when we double the potential difference
as the capacitance only depends on the geometry of the capacitor, hence it will not change
e. tilting one platge so that seperation is differnet at different ends
this will recude d for some part of the capactor, and hence will increase the capacitance
2. given
r = 8 cm
d = 1 mm
a. C = pi*r^2*epsion/d = 4*pi*epsilon*r^2/4d
C = r^2/8.9*10^9*4*1*10^-3
C = 1.79775*10^-10 F
b. V = 100 V
Q = ?
using
Q = CV
Q = 1.7977*10^-8 C
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