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Reluctance = $\dfrac{l_e}{\mu A_e}$ where..... mu is the absolute permeability of the material, $\mu_0 \mu_r $ $l_e$ is the circumference of a circle at a radius r and $A_e$ is a small cross sectional area. The circle I refer to only relates to the cross section of the torus and r is the radius from the centre (where the wire is). All these reluctances ...


Hint in a parallel circuit, the voltage across each resistor is the same. What is the voltage across the $4 \Omega$ resistor?


I think the shaking action causes the batteries to move slightly, thus 'scraping' the contact area on the batteries and the contact elements in the remote. This improves the conductivity, and so on. Certainly I've had success opening the battery compartment and physically rotating the batteries and/or scraping the contacts gently. I think it's unlikely ...

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