Solution

ID: past-exam-of-the-theoretical-physics-major-option-course-of-the-university-of-oxford/2022/3/d/solution

Count net transmitted charges per unit time, taking left-to-right as positive. The contact on the left, the internal bond, and the contact on the right give respectively
The backward rate must be subtracted in the internal count. Substitution of solution yields
The equalities also follow directly from and : there can be no stationary accumulation of electric charge. If each carrier has charge , the electric current is . During a stationary interval of duration , the expected net number crossing any one bond is . In particular, counting both directions of internal hopping as positive would count traffic, not transmitted charge.

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