You Do Need power plug adapter while traveling from Switzerland to Bhutan.

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G and in Switzerland are C and J. This is how they look like.

Switzerland

In Switzerland, outlets of type C and J are in use.

Type C

Type J

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G