When a voltage of one volt is applied, a circuit allows one micro ampere current to flow through it. The conductance of the circuit is

The correct answer is $\boxed{\text{B. }10^6 \text{ mho}}$.

Conductance is the inverse of resistance, and is measured in siemens (S). One siemens is equal to one ampere per volt (A/V). One microampere is equal to one millionth of an ampere (μA). Therefore, if a voltage of one volt is applied to a circuit and one microampere of current flows through it, the conductance of the circuit is $10^6 \text{ mho}$.

Option A is incorrect because one nanomho is equal to one billionth of a siemens (μS). Option C is incorrect because one millimho is equal to one thousandth of a siemens (mS). Option D is incorrect because it is not one of the possible answers.