COMPE 271
EE310 - Spring 2013 - Midterm Exam # 2
Friday, March 29th, 10am - 10:50 am
Instructions:
•
This examination is closed book, closed notes, and calculators/cellphones/laptops etc cannot be used.
By signing this document, you are pledging to adhere to the honor system stating that all work performed here is strictly your own effort.
•
•
Limited partial credit given for some problems. Check your answers carefully for arithmetic mistakes.
•
•
List all assumptions, show all work and clearly indicate your answer.
Only one answer will be considered; more than one answer is automatically graded incorrect. Work on top of an erasure will be not be reconsidered for any reason after the exam is returned; circle and draw a line through work to be discarded.
You have up to 50 minutes to take this examination. Good luck!
Name/Last 5 digits of RedID
Signature
________________________________________
____________________________________________________
Problem 1: Power in Sinusoidal Circuits (5 x 4 = 20pts.)
Find (i) the average power, (ii) the reactive power,
(iii) the complex power absorbed by the load in the circuit below and also (iv) the power factor
(numerical value and leading or lagging) if i g = 40 cos(5000t )mA.
P=
,Q=
, S =
, PF =
, leading/lagging (circle one)
Problem 2: Basics of Laplace Transforms (10 pts.)
Find L{t 2 e −2t + 10 sin( 3t + 45 o )} using only the Laplace transform pairs, the properties of the
Laplace transform (not the ones in the formula sheet, just what you are given below), and math identities that are provided below. a) sin(A+B) = sinAcosB + cosAsinB,
b)
1 ω s
L{e − at } =
, L{sin( ωt )} = 2
, L{cos(ωt )} = 2
, and
2
s+a s +ω s +ω2
dF c) L ∑ α k f k (t ) = ∑ α k Fk ( s ), and L{tf (t )} = − ds k
k
F ( s ) = L{t 2 e −2t + 10 sin(3t + 45o )} =
Problem 3: Initial/Final Value Theorems and Solving ODEs (3 + 7 + 4 = 15pts.)
&
&
x
a) For the
Friday, March 29th, 10am - 10:50 am
Instructions:
•
This examination is closed book, closed notes, and calculators/cellphones/laptops etc cannot be used.
By signing this document, you are pledging to adhere to the honor system stating that all work performed here is strictly your own effort.
•
•
Limited partial credit given for some problems. Check your answers carefully for arithmetic mistakes.
•
•
List all assumptions, show all work and clearly indicate your answer.
Only one answer will be considered; more than one answer is automatically graded incorrect. Work on top of an erasure will be not be reconsidered for any reason after the exam is returned; circle and draw a line through work to be discarded.
You have up to 50 minutes to take this examination. Good luck!
Name/Last 5 digits of RedID
Signature
________________________________________
____________________________________________________
Problem 1: Power in Sinusoidal Circuits (5 x 4 = 20pts.)
Find (i) the average power, (ii) the reactive power,
(iii) the complex power absorbed by the load in the circuit below and also (iv) the power factor
(numerical value and leading or lagging) if i g = 40 cos(5000t )mA.
P=
,Q=
, S =
, PF =
, leading/lagging (circle one)
Problem 2: Basics of Laplace Transforms (10 pts.)
Find L{t 2 e −2t + 10 sin( 3t + 45 o )} using only the Laplace transform pairs, the properties of the
Laplace transform (not the ones in the formula sheet, just what you are given below), and math identities that are provided below. a) sin(A+B) = sinAcosB + cosAsinB,
b)
1 ω s
L{e − at } =
, L{sin( ωt )} = 2
, L{cos(ωt )} = 2
, and
2
s+a s +ω s +ω2
dF c) L ∑ α k f k (t ) = ∑ α k Fk ( s ), and L{tf (t )} = − ds k
k
F ( s ) = L{t 2 e −2t + 10 sin(3t + 45o )} =
Problem 3: Initial/Final Value Theorems and Solving ODEs (3 + 7 + 4 = 15pts.)
&
&
x
a) For the