Awire with resistance r is connected to the terminals of a 30 v battery. part a what is the potential difference δvends between the ends of the wire?

30 V

Explanation:

When the wire is connected to the terminal of the battery, the potential difference across the wire becomes equal to the emf produced by the battery. This can be seen by using also Kirchhoff second law, which states that the sum of the p.d. across the components of a closed loop in a circuit must be equal to the sum of the emf of the batteries in the circuit:

In this case, we have

(there is only one battery)

Therefore,

and since there is only one resistor, it means that the p.d. across the resistor is 30 V.