  The choice of impedance used to shunt a Josephson junction determines if the
charge transferred through the circuit is quantized: a capacitive shunt renders
the charge discrete, whereas an inductive shunt leads to continuous charge.
This discrepancy leads to a paradox in the limit of large inductances L. We
show that while the energy spectra of the capacitively and inductively shunted
junction are vastly different, their high-frequency responses become identical
for large L. Inductive shunting thus opens the possibility to observe charging
effects unimpeded by charge noise.
