EXAM 2 A
PHYS 121
SAMPLE EXAM 3
SUMMER 2003
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The exam is closed book and closed notes.
Make sure you put your name on the SCANTRON form.
e = 1.6x10-19 C;
k
q 1q 2
;
r2
σ=
E=k
Q
A
q1
;
r2
∫
C=
ε0 A
d
dQ
dt
J=
i
A
∆U = -W = q∆V
C=
q encl
ε0
κε0 A
d
V
R=
i
∆V = - E⋅d
parallel: Ceq = C1+C2+…Cn
charging: Q = CV∞ (1-e-t/RC),
discharging:
k = 8.99x109 Nm2/C2;
Area = πr2
Φ = EdA =
Q
V
C=
i=
me = 9.11x10-31kg
Q = Q0 e-t/RC,
k=
σ
2ε 0
E=
λ
2πε 0 r
∫
 1
1
1
series : C eq = 
+
+ ...
Cn
 C1 C 2
ρL
R=
A
V
E=
d
point charge, sphere: V = k
E = ρJ
VC = V∞ (1-e-t/RC),
i = i0 (e-t/RC),
F=
∆V = − E ⋅ ds
Q2
1
U=
= C ⋅ V = CV 2
2C
2
j = (ne) vd
ε0 = 8.85x10-12 C2/ Nm2 ;
1 mega (1M ) = 106
1 m = 1000 mm
E=
1
;
4 πε 0
q1
r
parallel : R eq



−1
 1
1
1
= 
+
+ ...
Rn
 R1 R 2




−1
charged plane: V = V0 - Ex
ρ - ρ0 = ρ0α(T - T0) P = iV
P = i2R
series: R = R1 + R2+..Rn
i = i0 (e-t/RC), VR = i0 R (e-t/RC),
Vc = V0 (e-t/RC),
VR = i0 R (e-t/RC),
1. When electron moves from A to B along an electric field line, the electric filed
does 8 x 10-19 J work on it. What is the electric potential difference between VB VA?
A. 1 V
B. 3 V
C. 5 V
D. 7 V
E. 9 V
2. Four charges q = 4nC form a square, 20 cm on a side, as shown in figure below.
What is the potential at the center of the square ?
A. 360 V
B. 420 V
C. 510 V
D. 640 V
E. 700 V
q
-q
q
q
3. An electron is accelerated from rest through a potential difference of 2500 V. What is its final velocity?
A. 8x107 m/s
B. 3x107 m/s
C. 5x106 m/s
D. 8x105 m/s
E. 7x104 m/s
4. A hollow metal sphere is charged to a potential V. The potential at its center is:
A. V
B. 0
C. -V
D. 2V
E. -2 V
5. In a circuit capacitor C1 = 2nF is first charged by closing of switch S, and connecting it to battery of ∆V = 21 V. Switch S1 is then
opened, and charged capacitor is connected to the uncharged capacitor C2 = 5nC by closing switch S2. The final charge on C2 is
A. 10 nC
B. 20 nC
C. 30 nC
D. 40 nC
E. 50 nC
6. What maximum potential difference (before it breaks down) can be applied to an air filled parallel-plate capacitor C = 2 nF if the
surface area is 8x10 -4 m2? (dielectric strength of air is E = 3x106 V/m)
A. 2 V
B. 5 V
C. 7 V
D. 11V
E. 15 V
7. A battery is used to charge a parallel-plate capacitor, after which it is disconnected. Then the dielectric with κ=2 is inserted between the
plates. This process will:
A) half the capacitance
B) double surface charge density on each plate
C) half stored energy
D) double electric field between the two places
E) double charge on each plate
8. A 10-m long aluminum wire with a radius of 0.4 mm carries a current of 5 A. If resistivity of aluminum is 2.75x10-8 Ωm. what is the
potential difference across this wire?
A. 2.7 V
B. 8.6 V
C. 12.5 V
D. 18.2 V
E. 23.4 V
9. A 1.5-V potential difference is maintained across a 1.5-m length of tungsten wire that has a cross-sectional area of 0.6 mm2 and
resistivity of5.25x10-8 Ωm. How much power is dissipated in the wire?
A. 4 W
B. 8 W
C. 12 W
D. 15 W
E. 17 W
10. A potential difference of 3 nV is set up across a 2 cm length of copper wire that has a radius of 2 mm. How much charge drifts
through a cross section in 3 ms (e = 1.6x10-19C, resistivity of copper is 1.68x10-8Ωm)
A) 2.1.10-2
B) 5.4.10-2
C) 1.22.10-5
D) 3.4.10-7
E) 8.9.1017
11. A wire A and wire B are made from the same material. Wire A has twice the radius and half the length of wire B and resistance 8 Ω.
The resistance of wire B is:
A) 2 Ω.
B) 8 Ω.
C) 16 Ω.
D) 32 Ω.
E) 64 Ω.
12. The current in a 120-V heater is 12.5 A. If the cost of electrical energy is 15 cents per kilowatt-hour, how much does it cost to use the
lamp for 12 hrs.
A) 43 cents
B) 80 cents
C) 115 cents
D) 124 cents
E) 270 cents
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Workout problems. Show your work.
1. Four capacitors C1 = 15µF , C2 = 3µF , C3 = 6µF , C4 = 20µF are connected as shown.
Potential difference across the combination is Vab = 24 V
a) Find the equivalent capacitance between points a and b. Ans 6µ
µF _________
b) Find charge on C4 Ans 144µ
µC , ______________
µC , _______________
c) Find charge on C3 Ans_102µ
d) Find charge on C2 Ans 42µ
µC , ________________
e) Find charge on C1 Ans 42µ
µC , ________________
2. ( 3 points) A 20 mV potential difference is applied to a 10 m long copper wire of radius of 0.5 mm. The resistivity of copper is
1.68x10-8 Ωm .
A) What is the resistance of the wire? Ans: 0.21 ohms
B) What is the electric field in the wire? Ans: 2x10-3 V/m
C) What is the current density? Ans: 1.21x105 A/m2