Is it possible for a system to have negative potential energy?

Good morning.

Yes, it is possible.

Energy is a scalar quantity. The value of the potential energy is calculated the following way:



Where m is mass, g is the acceleration of gravity and h is the height.

Note that the height depends on the adopted referential, therefore, if we adopt, for example, a referential on the floor, if we dig a hole that has a depth of 1 meter, a ball that is put inside the hole will have negative potential energy due to the adopted referential, since h is negativa in this case.

Ohm's law tells you that i = v/r where v is equivalent voltage and r is equivalent resistance of the circuit
since all circuits have the same voltage, your question is really asking which circuit has the lowest total resistance, since the lower the resistance, the higher the current
circuit a has a resistance of 5 ohms; circuit c is in series so has a resistance of 10 ohms; circuit b is in parallel and therefore has a resistance of 2.5 ohms (review your notes on adding resistances in parallel and series); therefore b has the highest current