(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In the circuit shown in the following figure(Figure 1) the capacitor has capacitance 20 microF and is initially uncharged. The resistor R_0 has resistance 12 Ohms . An emf of 90.0V is added in series with the capacitor and the resistor. The emf is placed between the capacitor and the switch, with the positive terminal of the emf adjacent to the capacitor. The small circuit is not connected in any way to the large one. The wire of the small circuit has a resistance of 1.1 Ohm/m and contains 29 loops. The large circuit is a rectangle 2.0 m by 4.0 m, while the small one has dimensions a = 14.0cm and b = 25.0cm . The distance c is 3.0cm . (The figure is not drawn to scale.) Both circuits are held stationary. Assume that only the wire nearest the small circuit produces an appreciable magnetic field through it.

I found a picture of the figure here: http://www.chegg.com/homework-help/...citance-18-mu-f-initially-uncharged--q3009362.

1) The switch is closed at t = 0. When the current in the large circuit is 5.00A , what is the magnitude of the induced current in the small circuit?

2) What is the direction of the induced current in the small circuit?

2. Relevant equations

Equations with RC Circuits:

[tex]\tau = RC [/tex]

I=(Emf/R)e^(-t/RC)

Other Equations:

Magnetic Flux: [itex]\Phi[/itex] = Int(B*dA)

Faraday's Law: Emf_induced = -N(d([itex]\Phi[/itex])/dt)

3. The attempt at a solution

So, the first thing I did was try to find the time at which the current in the large circuit would be 5.00 A. I got the t = 9.73*10^-5 s.

What I'm stuck at now is how to figure out the change in flux with respect to time, or how to break it up so it is easier to solve. I think you might be able to use Ampere's law to draw an Amperian loop (so that you can figure out B), but I'm not sure what shape to use and where to draw the loop.

For the direction of the induced current in the small circuit, I know the induced current is supposed to result in a magnetic field that opposes the change in the magnetic flux that induces the current (so, the magnetic flux through the big circuit, right?) I'm thinking that the current is flowing cw in the big circuit, and the current decreases over time, so the magnetic flux would be decreasing into the big circuit, right? If that's the case, then the induced current in the small circuit would oppose that decreasing flux, so the induced current should also be clockwise, right? I guess my biggest uncertainty is that I don't know for sure (it says the positive terminal of the emf source is adjacent to the capacitor, so flowing from + to - should mean cw current, right?) which direction the current is flowing in the big circuit. Thank you!

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# Mutual Inductance of Two RC Circuits?

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