Final answer:
Approximately 1.95 14 AWG conductors can be installed in a 1 7/8 inches deep handy box if it is being used as a junction box.
Step-by-step explanation:
An older rule of thumb for installing conductors in a junction box is 5 side-to-side and 7-8 deep. However, newer recommendations suggest as much as 8 diameters side-to-side and 15 diameters deep. Since the box is 1 7/8 inches deep, we can use the newer recommendation of 15 diameters to determine the maximum number of conductors.
The diameter of a 14 AWG conductor is approximately 0.0641 inches. To fit 15 diameters side-to-side, we multiply 0.0641 inches by 15, which gives us 0.9615 inches. Since the box is 1 7/8 inches deep (or 1.875 inches), we can divide 1.875 by 0.9615 to find that approximately 1.95 conductors can be installed in the handy box.
Therefore, approximately 1.95 14 AWG conductors can be installed in the handy box if it is being used as a junction box.