Step 1: Understanding the Concept:
PBrCl\(_3\) has phosphorus as the central atom. Structure depends on arrangement.
Step 2: Detailed Explanation:
PBrCl\(_3\) can have different isomers. If all Cl atoms are in equatorial positions and Br in axial (or vice versa), the molecule may have zero dipole if symmetric.
From the given options in image, the isomer with symmetric distribution has no dipole.
Step 3: Final Answer:}
Thus, the isomer with trigonal bipyramidal geometry having all similar atoms in one plane has no dipole moment.