Homework Statement
Using an AC signal generator vs, a transformer with turns ratio n = 1, and a battery VB, sketch a circuit that will generate the output signal vout = vs + VB
Homework Equations
\frac{V_2}{V_1} = \frac{N_2}{N_1}
The Attempt at a Solution
Here's my sketch...
Homework Statement
a) Determine the impedance of this circuit.
b) What is the impedance when \omega = \frac{1}{\sqrt{LC}}
Homework Equations
The Attempt at a Solution
EDIT: I got the Z wrong. It's Z = \frac{L}{C(j{\omega}L - \frac{j}{{\omega}C})}
For part b, I'm...
Bah. I don't know why this is eluding me.
Here's where I am now:
dq= \frac{q}{4{\pi}r^2}da , da=2{\pi}rdr
therefore:
dq = \frac{q}{2r}dr
(Here r is the radius of the slice, I'll use R for radius of the sphere).
However I don't think that I have my da right. What's the...
Originally I thought that surface area would come into play, but I think that since we're worried about Current Areas maybe not? I feel like there should be a dq in there somewhere. So maybe two integrals?
Okay, so for the area, I could integrate from 0->R twice to sum all the cross-sectional areas of the sphere:
A = \pi r^2 therefore dA = 2{\pi}rdr
and
A_{total}=2\int_0^R \! 2{\pi}rdr
and A= 2{\pi}R^2
Now we have: \vec{\mu} = \frac{q}{T} \frac{2{\pi}R^2}{c} =...
Homework Statement
Show for a solid spherical ball of mass m rotating about an axis through its center with a charge q uniformly distributed on the surface of the ball that the magnetic moment \mu is related to the angular momentum
\vec{\mu}={\frac{5q}{6mc}}\vec{L}
Homework...
Homework Statement
Prove that the spherical harmonic wave function \frac{1}{r}e^{i(kr-{\omega}t)} is a solution of the three-dimensional wave equation, where r = (x^2+y^2+z^2)^{\frac{1}{2}} . The proof is easier if spherical coordinates are used.
Homework Equations
Wave function...
Well let's see:
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
Which I got to:
\frac{1}{R_{eq}} = \frac{R_1R_2 + R_1R_3 + R_2R_3}{R_1R_2R_3}
Which means:
R_{eq} = \frac{R_1R_2R_3}{R_1R_2 + R_1R_3 + R_2R_3}
Then I'd plug that in V = IR_{eq} and get:
V =...
Thanks for the quick reply! I see where you're getting at - makes the math much simpler, but we haven't covered conductance yet. Is there any other way around the problem, or do I just have to do some nasty algebra?
Homework Statement
Hey everyone. I might be overthinking this one, but I thought I'd post it. (sorry for the crappy MS Paint sketch!)
I need to find the current through R3
Homework Equations
V=IR
\SigmaV=0 (around a closed loop)
\SigmaI=0 (going into a junction)
The Attempt...