Question #88201

A galvanometer of resistance $G$ (in $\Omega$) and full-scale deflection current $I_g$ (in A) is converted into an ammeter of range $I_0$ (in A) by connecting a cylindrical metal rod as a shunt in parallel. The shunt rod is rigidly fixed between two unyielding, perfectly insulating walls such that its length cannot change. The rod has an initial resistivity $\rho_0$ (in $\Omega\cdot$m), temperature coefficient of resistivity $\alpha$ (in K$^{-1}$), coefficient of linear thermal expansion $\lambda$ (in K$^{-1}$), and Poisson's ratio $\nu$ (dimensionless). If the temperature of the shunt rod is uniformly increased by $\Delta T$ (in K) while the galvanometer remains at a constant temperature, what is the new maximum current $I'$ (in A) that this ammeter can measure? Assume $\alpha \Delta T \ll 1$ and $\lambda \Delta T \ll 1$.