Question #43374

A metre bridge is set up to measure an unknown resistance. The left gap contains a standard resistor $R = 10\ \Omega$ and the right gap contains a resistor $S = 30\ \Omega$. The uniform metre bridge wire has a length of $100\ \text{cm}$ and a total resistance $R_w = 10\ \Omega$. The bridge is powered by a battery of electromotive force $E = 24\ \text{V}$ in series with an internal resistance $r = 4\ \Omega$. The null detector consists of a galvanometer shunted by a dynamic non-linear resistor whose resistance varies with the galvanometer current $I_g$ as $R_{sh} = \frac{50}{1 + \lambda|I_g|}\ \Omega$, where $\lambda = 100\ \text{A}^{-1}$. Due to local heating at the contacts, the end corrections of the metre bridge depend on the steady current $I_w$ flowing through the bridge wire. The left end correction is given by $\alpha = (2.5\ \text{cm/A}) I_w$ and the right end correction is $\beta = (1.25\ \text{cm/A}) I_w$. Determine the null point $l$ measured from the left end of the bridge wire.