CALENG3 Flashcards
A network with only one closed path
Electric Circuit
The algebraic sum of voltage drops around a loop or electric circuit is zero
Kirchoff’s Law
Voltage supplied = ___________
Sum of voltage drops
The voltage drop across a/an __________ is proportional to the current passing through the component
Resistor
The voltage drop across a/an ___________ is proportional to the instantaneous time rate of charge of the component
Inductor
The voltage drop across a/an ____________ is proportional to the instantaneous electric charge on the component.
Capacitor
Time when isotope/substance reach half of its original amount
Half-Life
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
All of the above
The time rate of change of the electric charge is called the instantaneous _______ .
Current
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.
Newton’s Law of Cooling
______ is an element of an electric circuit which tends to oppose the change of current across it
Inductor
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.
D
Name the units of the following:
1. Electromotive Force or Voltage
2. Resistor
3. Inductor
4. Capacitor
5. Charge
6. Current
- Volts
- Ohms
- Henry
- Farads
- Coulombs
- Ampere
If r1 is greater than r2, what will happen to the solution in the tank?
Overflow
if r1 is less than r2, what will happen to the solution in the tank?
Depletion of Solution
if r1 is equal to r0, what will happen to the tank?
No change in volume
Formula for Growth and Decomposition
dx/dt = kx ; X= Ce^kt
Formula for Newton’s Law of Cooling
dT/dt = k(T-T0) ; T = T0 + Ce^kt
Formula for Chemical Solutions
dx/dt = rici - roco; c0 = x/v; V = v0+(ri-ro)t
Formula for RL Circuit
L di/dt + iR = E
Formula for RC Circuit
R dQ/dt + Q/C = E ; i = dQ/dt
Formula for Logistic Equation
dx/dt = k(a-x) x
In a homogeneous equation, if M is simpler, what would be the appropriate substitution?
Let x=vy; dx = vdy + ydv
In a homogeneous equation, if N is simpler, what would be the appropriate substitution?
Let y=vx; dx = vdx + xdv
In an exact differential equation, how do you test for exactness?
dM/ dy = dN / dx
where d= partial derivative
Formulas for First Order Linear Differential Equation
Form: dy/dx + P(x)y = Q(x) —> Linear in Y
Form: dx/dy + P(y)x = Q(y) —> Linear in X
Order of Checking for First order Linear DE
VS
Homogeneous
Exact
Linear (linear in a variable, linear in a function)
Bernoulli’s
Substitution suggested by the equation
In the Wronskian Method, the functions are considered to be linearly dependent and linearly independent under what conditions?
If W(x) equals 0, they are linearly dependent.
If W(x) does not equal 0, they are linearly independent.
The Wronskian was created by _______ .
Jozef Maria Hoene-Wronski
In using Method of Undetermined Coefficients, the following types for R(x) can be __________________ , otherwise use Variation of Parameters
Polynomial
Exponential
Sine Function
Cosine Function
Quadratic formula
(-b +- sqrt(b^2-4ac) )/ 2a
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) ) .
True
Derivative of ln x
1/x
Laplace Transform of t^n f(t)
(-1)^n F^n (s)
Laplace Transform of tcos(kt)
(s^2-k^2) / (s^2+k^2)^2
Laplace Transform of tsin(kt)
(2ks) / (s^2+k^2)^2
Laplace Transform of sin(kt)-ktcos(kt)
(2k^3) / (s^2+k^2)^2
Half Angle formula for sin^2 t
(1-cos 2t) / 2
Half Angle formula for cos^2 t
(1+cos 2t) / 2
Formula for Bernoulli’s
Form: dy / dx + P(x)y = Q(x)^n
IF: e^int(1-n)P(x)dx
