All Problems

Electric Current

Problem 3.156

The space between two conducting concentric spheres of radii \(a\) and \(b(a < b)\) is filled up with homogeneous poorly conducting medium. The capacitance of such a system equals \(C .\) Find the resistivity of the medium if the potential difference between the spheres, when they are disconnected from an external voltage, decreases \(n\) -fold during the time interval \(\Delta t\).

Reveal Answer
ρ=4πΔtab/(ba)Clnη\rho=4 \pi \Delta t a b /(b-a) C \ln \eta