In the given circuit the resistance of slider PQ is zero. It starts sliding at $\mathrm{t} = 0$ from the shown position with a uniform speed $v_0$, AC, BD are uniform wires of resistance $\mathrm{\lambda }{\mathrm{\Omega m}}^{-1}$. If in the duration from $\mathrm{t}=0$ to $\mathrm{t} =1\mathrm{s}$ the charge flown through the slider is $\ln \left(\frac{3}{2}\right)$ coulomb, $\mathrm{\lambda }$ is ____.