Question #43372

A potentiometer wire $AB$ of length $L = 1.0 \text{ m}$ and uniform cross-sectional area $A$ is connected to a primary ideal cell of electromotive force $E_0 = 16 \text{ V}$ and zero internal resistance. The wire $AB$ is subjected to a non-uniform temperature distribution along its length given by $T(x) = T_0 + \Delta T \left(\frac{x}{L}\right)^2$, where $x$ is the distance from end $A$. The resistivity of the wire varies with temperature as $\rho(T) = \rho_0 [1 + \alpha(T - T_0)]$. Given that the product of the temperature coefficient of resistivity $\alpha$ and $\Delta T$ is $\alpha \Delta T = 3.0$. A secondary cell of electromotive force $E_1 = 5.0 \text{ V}$ and internal resistance $r = 1.0 \ \Omega$ is connected to a galvanometer to find the null point on the wire $AB$. Find the distance $x$ from end $A$ where the galvanometer shows zero deflection.