Three timer consider three vacuum filled parallel

31. Three timer. Consider three vacuum-filled parallel-plate capacitors, each with charge Q ,
whose properties are listed in the table shown. Which of the following is the correct rela-
tionship among the energies stored in each capacitor?
Capacitor Area Separation Distance
X 2 A 3 d
Y 4 A d/ 5
Z A/ 5 2 d
A. U
X
< U
Y
< U
Z
B. U
Z
< U
Y
< U
X
C. U
Z
< U
X
< U
Y
D. U
Y
< U
X
< U
Z
Solution:
The capacitance of the parallel-plate capacitor is
C = ε
0
A
d
and the energy stored in the capacitor is
U =
1
2
Q
2
C
=
dQ
2
2 ε
0
A
Therefore, the energy stored in each capacitor is
U
Capacitor X
3
2
dQ
2
2 ε
0
A
Capacitor Y
1
20
dQ
2
2 ε
0
A
Capacitor Z 10
dQ 2
2 ε
0
A
A – 17

Sample Exam Second Semester, AY 2016–2017 Physics 72
32. Kwatro Kantos. What happens to the energy density inside a vacuum-filled parallel-plate
capacitor if the electric field magnitude between the plates is increased by a factor of 4 ?
33. Capacitance. A spherical vacuum-filled capacitor with inner and outer radii of R and 2 R ,
respectively, has a capacitance of C . If the outer radius is increased to 3 R , what will be the
new capacitance?

Sample Exam Second Semester, AY 2016–2017 Physics 72
35. Can you handle my drift? A current is travelling along a wire. The cross-sectional
area of the wire suddenly increases by 15% . If the current and the free-electron density
are maintained, what is the new drift velocity of the electrons in terms of the initial drift
velocity ~ v
d
?