a, b < 0 which means ω < 0. So:
\frac{1}{iw}e^{iwt}\biggr|_0^{\infty} = -\frac{1}{iω} for ω < 0.
From that, the complete answer to the original integral is:
-\frac{2e^{2}}{jω} = \frac{j2e^{2}}{ω} for ω < 0.
Thanks for the help! If I made any mistakes above, let me know.
Since the 5 ohm resistor can be removed (it's shorted), the 3 ohm and the 6 ohm resistors are in ______? (try redrawing the circuit with the 5 ohm resistor removed)
I do not understand the following integral:
\int^{\infty}_{0}2e^{2+jωt}dt = \frac{j2e^{2}}{\omega}
Why is it not ∞? Here are my steps:
Let u = 2+jωt, du = jωdt, dt = \frac{1}{jω}du = -\frac{j}{ω}du
\int^{\infty}_{0}2e^{2+jωt}dt
= -\frac{2j}{ω}\int^{\infty}_{2}2e^{u}du
=...
I just noticed that the time scale for 4 < t < 5 remains the same for the figure in the book. I know the time scale is compressed by 0.5 up until t = 4. So, is the book's figure supposed to look like my plot instead? It seems impossible to express y(t) as a function of x(t) if I use the figure...
Homework Statement
Express y(t) as a function of x(t).
https://www.physicsforums.com/attachment.php?attachmentid=61309&d=1378005939
Homework Equations
The Attempt at a Solution
Transformations:
-x(t)
0.5x(t)
x(2t)
x(t-2)
x(t)+1.5
∴y(t) = -0.5x(2t-4)+1.5
Here is the plot...
I can't seem to remember how to find the amplitude/phase of a complex function (I do know what to do for complex numbers, though). I know it's in my mind somewhere, but I just can't remember lol. So, for example, how would I find the amplitude/phase of:
3+j5t
and
3ej4t
EDIT: I know for...
I did all that, but still no go. It's odd that I wasn't the only one that could not get the design for the xor using 4 nand gates working (was a lab). They had the same problems.
The logic diagram is attached. I made the four NAND gates using four 4007s and then the inverter uses the first 4007 (pins 9, 10, 11, 12). Someone else made the circuit using five NAND gates and they have the same issue (S output is the inverted C output).
I also found a top view of the 4007...
I have an issue with the outputs from a half-adder. I am using three CD4007UBE chips and the outputs always stay at zero. I simulated using a model for the CD4007, and it worked without any issues. However, the actual circuit's outputs remain zero for every input.
The input signals are A and...
Homework Statement
A 1-cm cube of p-type silicon (ρ = 0.1Ω-cm) acquires a linear electron distribution in the x-direction, such that n = 1014/cm3 at one side and n = 105/cm3 at the opposite side.
Wires are attached to the sides of the cube via ohmic contacts, and a 0.1mV voltage source is...
Homework Statement
A certain doped semiconductor at room temperature has the following properties: no = 9 x 1014 / cm3, po = 4 x 1014 / cm3, μe = 800 cm2 / V-s, μh = 400 cm2 / V-s, and (Dh\tauh)1/2 = 10-4 cm.
If an electric field is applied, what fraction of the resulting drift current flow...
Maybe I'm blind, as I don't see what it would simplify to. Would it cause RB + RE to be ignored in the denominator? Then, the two beta values would cancel from the top/bottom? So:
\frac{(V_{in} - V_{f})R_{C}}{R_{E}}
Oh, oops. Vout = VCC - iCRC, so:
Vout = VCC - \frac{V_{in} - V_{f}}{R_{B} + R_{E}(1 + β_{F})}RCβF
I still don't see what it would reduce to with a large beta :|.