Question #43373

A metre bridge is constructed using a non-uniform wire of length $L = 100 \text{ cm}$. The resistance per unit length of the wire varies linearly as $\lambda(x) = \lambda_0 (1 + \gamma x)$, where $x$ is the distance from the left end and $\gamma = 0.01 \text{ cm}^{-1}$. The contact resistances at the left and right ends are $R_L$ and $R_R$ respectively. It is given that $R_L$ is equal to the resistance of a length $\alpha = 10 \text{ cm}$ of the bridge wire if it had a uniform resistance per unit length equal to that at the left end ($x=0$). Similarly, $R_R$ is equal to the resistance of a length $\beta = 8 \text{ cm}$ of the bridge wire if it had a uniform resistance per unit length equal to that at the right end ($x=100 \text{ cm}$). If two equal resistors are connected in the left and right gaps of the metre bridge, at what distance $x$ from the left end will the null point be obtained?