To solve the problem of finding the current in a platinum wire with a resistance of [tex]\(15 \, \Omega\)[/tex] when connected across a battery, we can use Ohm's Law. Ohm's Law is a fundamental principle used in electrical circuits, stating that the current ([tex]\(I\)[/tex]) flowing through a conductor between two points is directly proportional to the voltage ([tex]\(V\)[/tex]) across the two points and inversely proportional to the resistance ([tex]\(R\)[/tex]) of the conductor. The formula is given by:
[tex]\[ I = \frac{V}{R} \][/tex]
The problem states that the resistance [tex]\(R\)[/tex] of the platinum wire is [tex]\(15 \, \Omega\)[/tex]. Additionally, we must know the voltage [tex]\(V\)[/tex] across the wire to calculate the current. Let's assume the voltage [tex]\(V\)[/tex] is [tex]\(75 \, \text{volts}\)[/tex].
Then we can substitute the values into Ohm's Law:
[tex]\[ I = \frac{75 \, \text{volts}}{15 \, \Omega} \][/tex]
By performing the division, we get:
[tex]\[ I = 5 \, \text{amps} \][/tex]
Therefore, the current in the wire is:
[tex]\[ \boxed{5.0 \, \text{amps}} \][/tex]
So, the correct answer is:
[tex]\[ 5.0 \, \text{amps} \][/tex]
