Download Fall 2006

IMP 113: Final Exam Part I (Union College: Spring 2008)
Instructions:
1. Read all directions.
2. In keeping with the Union College policy on academic honesty, you should neither accept nor
provide unauthorized assistance in the completion of this work.
Name:__________________________________
Date:______________
Direction I: Solve the following Problems. In order to get full credit show all your work and
justify your reasoning.
1. A charge q is enclosed by several surfaces as shown in the figure. Find
a. the total electrical flux through the surface S1 if the charge q =
2C.
b. the total electrical flux through the surface S1 if the charge q =
4C.
c. the total electrical flux through the surface S1 if the charge q = 6C.
d. the total electrical flux through the surface S2 if the charge q = 2C .
e. the total electrical flux through the surface S3 if the charge q = 2C.
2. The potential in a region due to an Electric field is V  3xy 2  2 xz 2  5 , where x,y, and z are the
coordinates and are measured in meters, and the potential is measured in Volts.
a. Find the potential at the origin.
b. Find the potential at x=2m, y= 1 m, and z = 5 m.
c. Find the electric field at any point.
d. Find the electric field x=2m, y= 1 m, and z = 5 m.
3. Six capacitors are connected in a combination of series and parallel as shown in the figure
below. All of the capacitors are measured in micro Farads. (F)
a. Find the equivalent capacitance of the system
b. If a potential difference of 12 V is applied between terminal a and b, what is the charge
stored in the capacitor measured 3 F?
c. If a potential difference of 12 V is applied between terminal a and b, what is the charge
stored in the capacitor measured 2 F?
4. Given the circuit below.
a. Using Kirchhoff’s rules, write down the
system of linear equations for the three
currents in the circuit. Remember to show
all of your work.
b. Using Gauss-Jordan elimination, solve I1, I2, and I3. If you do not wish to use your
equations from part (a), use I1-I2+I3 = 0; I2+I3 = 6; and I1+2I2+I3 = 15.