Question

The current in a simple electrical circuit is inversely proportional to the resistance if the current is 40 amperes when the resistance is 6 ohms find the current when the resistance is 7.8 ohms

Answer 1

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:

`I=(k)/(R)`

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:

`\begin{gathered} I=(k)/(R) \\ 40=(k)/(6) \\ \text{Simplify and rearrange} \\ k=40(6) \\ k=240 \end{gathered}`

Next, we plug in k=240 and R=7.8 into I=k/R:

`\begin{gathered} I=(k)/(R) \\ I=(240)/(7.8) \\ \text{Simplify} \\ I=30.77\text{ amperes} \end{gathered}`

Therefore, the current is 30.77 amperes when the resistance is 7.8 ohms.