Recent content by hitemup

Homework Statement Let us have ##n \geq 3## points in a square whose side length is ##1##. Prove that there exists a graph with these points such that ##G## is connected, and $$\sum_{\{v_i,v_j\} \in E(G)}{|v_i - v_j|} \leq 10\sqrt{n}$$ Prove also the ##10## in the inequality can't be replaced...

@gneill Thank you for your comprehensive explanation about the input and output impedances and what they are good for. I understand these components avoid some bad conditions that may occur. However, I still wonder how the invertion is done in a NOT gate in the second figure, or I don't know if...

@Wee-Lamm If we can change the voltage from high to low and vice versa by using a dependent voltage source, then what's the use of capacitor and resistors in the circuit? One more question: where is v_cc in the second figure? I understand how a not gate works but I couldn't see what is...

Homework Statement [/B] I am studying a book related to digital integrated circuits and there is something I cannot understand. The book starts by explaining two basic building blocks of digital integrated circuits: the inverter and the non-inverter. My question is about the inverter. It...

Homework Statement [/B]Homework Equations [/B] Node-voltage method mesh current methodThe Attempt at a Solution [/B] My problem is with the short-circuit current. There are three meshes when you join the nodes a and b. Let i1 be the cw current for the bottom right mesh, i2 be the ccw...

Homework Statement [/B]Homework Equations The Attempt at a Solution I've highlighted two equations on the screenshot. How did it proceed from the first to the second? I'm actually confused with the absolute values. What is the idea behind getting rid of the first absolute value(1-5v^2) while...

Yes I realized at one time it would be easier if I used cylindrical coordinates, since the region itself is a cylinder. But I just wanted to know how to proceed with spherical coordinates.

Homework Statement Evaluate \int \int \int _R (x^2+y^2+z^2)dV where R is the cylinder 0\leq x^2+y^2\leq a^2, 0\leq z\leq h Homework Equations [/B] x = Rsin\phi cos\theta y = Rsin\phi sin\theta z = Rcos\phiThe Attempt at a Solution [/B] 2*\int_{0}^{\pi/2}d\phi \int_{0}^{2\pi}d\theta...

I learned it in high school and it was only for integers. This is something new but I'll try to handle it, thank you. What exactly has to be done after writing the series expansion?

Homework Statement I am asked to show that B = \frac{\mu_0Q\omega}{2\pi R^2}[\frac{R^2+2x^2}{(R^2+x^2)^{1/2}}-2x] simplifies to this B \approx \frac{\mu_0}{2\pi}\frac{\mu}{x^3} if x>>R where \mu is the magnetic dipole moment for a disk spinning with angular velocity \omega, which is \mu...

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c3 This is the same formula except pi*r^2*I is changed with mu(magnetic dipole moment) in mine.

Homework Statement The Earth's magnetic field is essentially that of a magnetic dipole. If the field near the North Pole is about 10^-4 T, what will it be (approximately) 13,000 km above the surface at the North Pole? Homework Equations B = \frac{\mu _0}{2\pi}\frac{\mu}{(R^2+x^2)^{3/2}} for...

So there is not any difference between forming the matrix as whether rows or columns and then row reduce, is there? EDIT: It turns out we can do it in both ways as you suggest, thank you.

Homework Statement A. Let {t,u,v,w} be a basis for a vector space V. Find dim(U) where U = span{t+2u+v+w, t+3u+v+2w, 3t+4u+2v, 3t+5u+2v+w} B. Compute the dimension of the vector subspace V= span{(-1,2,3,0),(5,4,3,0),(3,1,1,0)} of R^4Homework EquationsThe Attempt at a Solution I know that...

Sorry but that doesn't answer my question.