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Sagot :
Given the word problem, we can deduce the following information:
1. The current in a simple electrical circuit is inversely proportional to the resistance.
2. If the current is 40 amperes, the resistance is 6 ohms.
To determine the current when the resistance is 7.8 ohms based on the given information, we use the formula:
[tex]I=\frac{k}{R}[/tex]where:
I=current
k=constant
R=resistance
We plug in I=40 and R=6 into I=k/R to find the value of k:
[tex]\begin{gathered} I=\frac{k}{R} \\ 40=\frac{k}{6} \\ \text{Simplify and rearrange} \\ k=40(6) \\ k=240 \end{gathered}[/tex]Next, we plug in k=240 and R=7.8 into I=k/R:
[tex]\begin{gathered} I=\frac{k}{R} \\ I=\frac{240}{7.8} \\ \text{Simplify} \\ I=30.77\text{ amperes} \end{gathered}[/tex]Therefore, the current is 30.77 amperes when the resistance is 7.8 ohms.
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