CALENG3

Question 1

A network with only one closed path

Answer 1

Electric Circuit

Question 2

The algebraic sum of voltage drops around a loop or electric circuit is zero

Answer 2

Kirchoff’s Law

Question 3

Voltage supplied = ___________

Answer 3

Sum of voltage drops

Question 4

The voltage drop across a/an __________ is proportional to the current passing through the component

Answer 4

Resistor

Question 5

The voltage drop across a/an ___________ is proportional to the instantaneous time rate of charge of the component

Answer 5

Inductor

Question 6

The voltage drop across a/an ____________ is proportional to the instantaneous electric charge on the component.

Answer 6

Capacitor

Question 7

Time when isotope/substance reach half of its original amount

Answer 7

Half-Life

Question 8

From Kirchoff’s Voltage Law, we can conclude that:
(a) The algebraic sum of the voltages around the loop or electric circuit is zero
(b) The voltage supplied is equal to the sum of the voltage drops.
(c) Voltage Rise = Voltage Fall
(d) All of the above

Answer 8

All of the above

Question 9

The time rate of change of the electric charge is called the instantaneous _______ .

Answer 9

Current

Question 10

The rate at which the temperature of a body changes is directly proportional to the difference of the temperature of the medium from that of the body itself.

Answer 10

Newton’s Law of Cooling

Question 11

______ is an element of an electric circuit which tends to oppose the change of current across it

Answer 11

Inductor

Question 11

Which of the following is NOT TRUE about a resistor?
(a) The voltage drop is proportional to the amount of current flowing across it
(b) It is classified as a passive element in an electric circuit
(c) It resists the flow of the current across it.
(d) Voltage Drop = constant times the amount of electric charge across it
(e) None of the Above.

Answer 11

D

Question 12

Name the units of the following:
1. Electromotive Force or Voltage
2. Resistor
3. Inductor
4. Capacitor
5. Charge
6. Current

Answer 12

1. Volts
2. Ohms
3. Henry
4. Farads
5. Coulombs
6. Ampere

Question 13

If r1 is greater than r2, what will happen to the solution in the tank?

Answer 13

Overflow

Question 14

if r1 is less than r2, what will happen to the solution in the tank?

Answer 14

Depletion of Solution

Question 15

if r1 is equal to r0, what will happen to the tank?

Answer 15

No change in volume

Question 16

Formula for Growth and Decomposition

Answer 16

dx/dt = kx ; X= Ce^kt

Question 17

Formula for Newton’s Law of Cooling

Answer 17

dT/dt = k(T-T0) ; T = T0 + Ce^kt

Question 18

Formula for Chemical Solutions

Answer 18

dx/dt = rici - roco; c0 = x/v; V = v0+(ri-ro)t

Question 19

Formula for RL Circuit

Answer 19

L di/dt + iR = E

Question 20

Formula for RC Circuit

Answer 20

R dQ/dt + Q/C = E ; i = dQ/dt

Question 21

Formula for Logistic Equation

Answer 21

dx/dt = k(a-x) x

Question 22

In a homogeneous equation, if M is simpler, what would be the appropriate substitution?

Answer 22

Let x=vy; dx = vdy + ydv

Question 23

In a homogeneous equation, if N is simpler, what would be the appropriate substitution?

Answer 23

Let y=vx; dx = vdx + xdv

Question 24

In an exact differential equation, how do you test for exactness?

Answer 24

dM/ dy = dN / dx

where d= partial derivative

Question 25

Formulas for First Order Linear Differential Equation

Answer 25

Form: dy/dx + P(x)y = Q(x) —> Linear in Y
Form: dx/dy + P(y)x = Q(y) —> Linear in X

Question 26

Order of Checking for First order Linear DE

Answer 26

VS
Homogeneous
Exact
Linear (linear in a variable, linear in a function)
Bernoulli’s
Substitution suggested by the equation

Question 27

In the Wronskian Method, the functions are considered to be linearly dependent and linearly independent under what conditions?

Answer 27

If W(x) equals 0, they are linearly dependent.
If W(x) does not equal 0, they are linearly independent.

Question 28

The Wronskian was created by _______ .

Answer 28

Jozef Maria Hoene-Wronski

Question 29

In using Method of Undetermined Coefficients, the following types for R(x) can be __________________ , otherwise use Variation of Parameters

Answer 29

Polynomial
Exponential
Sine Function
Cosine Function

Question 30

Quadratic formula

Answer 30

(-b +- sqrt(b^2-4ac) )/ 2a

Question 31

True or False. We must use Variation of Parameters when R(x) is given as a fraction despite it containing exponential functions (ex. e^2x/ (1+e^2x) ) .

Answer 31

True

Question 32

Derivative of ln x

Answer 32

1/x

Question 33

Laplace Transform of t^n f(t)

Answer 33

(-1)^n F^n (s)

Question 34

Laplace Transform of tcos(kt)

Answer 34

(s^2-k^2) / (s^2+k^2)^2

Question 35

Laplace Transform of tsin(kt)

Answer 35

(2ks) / (s^2+k^2)^2

Question 36

Laplace Transform of sin(kt)-ktcos(kt)

Answer 36

(2k^3) / (s^2+k^2)^2

Question 37

Half Angle formula for sin^2 t

Answer 37

(1-cos 2t) / 2

Question 38

Half Angle formula for cos^2 t

Answer 38

(1+cos 2t) / 2

Question 39

Formula for Bernoulli’s

Answer 39

Form: dy / dx + P(x)y = Q(x)^n
IF: e^int(1-n)P(x)dx