Final answer:
For an inductor with half the original inductance and three times the current, the stored energy would be 9 Uo/4, calculated by modifying the formula U = (1/2) L I² to reflect the new inductance and current.
Step-by-step explanation:
The energy stored in an inductor can be determined by the formula U = (1/2) L I², where U is the energy, L is the inductance, and I is the current through the inductor.
For the given inductor with stored energy Uo, inductance Lo, and current Io, the energy is Uo = (1/2) Lo Io².
When the inductance is halved and the current is tripled, the new energy Uˉ can be calculated using the new values, giving us Uˉ = (1/2) (Lo/2) (3Io)² = (1/2) (Lo/2) (9Io²) = (9/4) (1/2) Lo Io² = (9/4) Uo.
Therefore, the energy stored in the inductor with half the inductance and three times the current is 9/4 times the original energy Uo, which is 9 Uo/4.