In the figure given, the value of X resistance when the potential differences between B and D is zero, is

Solution:

Potential difference between B and D is zero, it means Wheatstone bridge is in balanced condition.

$\mathrm{So}\frac{\mathrm{P}}{\mathrm{Q}}=\frac{\mathrm{R}}{\mathrm{S}}\Rightarrow \frac{21}{3+\frac{8\mathrm{X}}{\left(8+\mathrm{X}\right)}}=\frac{18}{6}\Rightarrow \mathrm{X}=8\mathrm{\Omega }$