A stationary circular wire loop with fixed electrical resistance \(R\) is placed in a uniform magnetic field directed perpendicular to the plane of the loop. The magnitude of the magnetic field changes monotonically from an initial value \(B_i\) to a final value \(B_f\) over an elapsed time interval \(\Delta t\). An experimenter observes that when the transition occurs over a very short time interval, the peak induced current is substantially greater than when the transition occurs over a long time interval, yet the total electric charge passing through a cross section of the wire is identical in both trials. Which of the following statements provides the physically correct explanation for why the total charge transferred is independent of \(\Delta t\)?