Question

when normal reaction is double, the coefficient of friction is

Answer 1

The coefficient of friction only depends on the nature of surfaces.

we can write a equation for friction force,

  friction force = coefficient of friction X normal force

                     F = μ X R

μ is constant for surface. Then we can write, Friction is propositional to the normal force. F α R

If you double normal force,friction force also double with that.

R->2R then F-> 2F    

Answer 2

when normal reaction is double , then coefficient of friction remains constant.

actually, coefficient of friction is proportionality constant. e.g., $fr\propto N$
$\implies fr=\mu N$
here $\mu$ is not other than coefficient of friction.
coefficient of friction depends only on roughness of contacting surface. higher the roughness , higher will be coefficient of friction.