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Probably a Kirchhoff's laws problem

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Two infinitely long solenoids (seen in cross-section) thread a circuit as shown in the figure below.

    http://capa.physics.mcmaster.ca/figures/sb/Graph31/sb-pic3152.png [Broken]

    Assume that L1 = 0.473 m, L2 = 0.473 m, H = 0.473 m, r1 = 0.112 m, r2 = 0.154 m, R1 = 6.13 Ω, R2 = 5.10 Ω and R3 = 3.28 Ω. The magnitude of B inside each is the same and is increasing at the rate of 122 T/s. What is the current in resistor R1?

    2. Relevant equations

    I believe the relevant equations to this are:

    [tex]\epsilon[/tex] = [tex]\frac{d\oint Bda}{dt}[/tex]

    Where it can be broken down into:

    [tex]\epsilon[/tex] = [tex]\frac{BA}{t}[/tex]

    That's how I'm trying to get the voltage for the loops.

    3. The attempt at a solution

    I'm trying it with the following voltage loops where the current runs up R2 and branches into the current going to R1 and R3.

    So far I've set up the following voltage loops, both taken going clockwise:

    (I've made the B/t equal to just G since it is given)

    G*pi*[tex]r1^{2}[/tex] + R2I2 + R1I1 = 0

    G*pi*[tex]r2^{2}[/tex] - R3I3 - R2I2 = 0

    I2 = I1 + I3

    I keep rearranging everything for I1, but it keeps coming out wrong. Could anyone perhaps tell me what I've done wrong in setting up my equations? I find this question rather confusing since we really haven't done much with induced currents in circuits.

    Any help would be greatly appreciated.

    Thanks!

    P.S. Whoever is in charge here should consider fixing that problem where a new template is added every time I preview my post... it's very annoying.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 17, 2009 #2
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