Some Electricity Questions

[bon]

Homework Statement

1) Where I(t) = Iocoswt, and V' is the voltage across an inductance V' = L dI/dt, I am asked to work out the time average of <I V' >..

when i work it out, the answer comes to zero...any ideas why?

2)I'm asked to sketch I(t) = Acos(w1 t)cos(w2 t) where w2 << w1...

is this just fast oscillations of speed (w2) within a boundary that is itself oscillating (more slowly..) ? so a cos graph within a cos graph with bigger period?

3) Find the bandwith of the signal I(t) = A cos^2 (wt) cos(10wt)..

I know bandwith is the randge of angular frequencies present in I, but here its not just 10wt-wt is it? How do I work it out?

Homework Equations

The Attempt at a Solution

 

[bon]

no ideas?

 

[bon]

anyone?

 

[willem2]

Homework Statement

1) Where I(t) = Iocoswt, and V' is the voltage across an inductance V' = L dI/dt, I am asked to work out the time average of <I V' >..

when i work it out, the answer comes to zero...any ideas why?

No power is dissipated in a network with only inductors and capacitors.

2)I'm asked to sketch I(t) = Acos(w1 t)cos(w2 t) where w2 << w1...

is this just fast oscillations of speed (w2) within a boundary that is itself oscillating (more slowly..) ? so a cos graph within a cos graph with bigger period?

yes

3) Find the bandwith of the signal I(t) = A cos^2 (wt) cos(10wt)..

I know bandwith is the randge of angular frequencies present in I, but here its not just 10wt-wt is it? How do I work it out?

cos^2 (wt) is also a product of two cosines, so you can replace it with a sum involving
cos (0) and cos (2wt)

 

[bon]

No power is dissipated in a network with only inductors and capacitors.


yes



cos^2 (wt) is also a product of two cosines, so you can replace it with a sum involving
cos (0) and cos (2wt)

Just a quick questionn about I = Acos(w1 t)cos(w2 t) one..

so w2 << w1 so would w2 be the outer shell, and w1 be the inner, fast oscillations.. how would you describe this?