The current in an electrical conductor varies inversely as the resistance of the
conductor. If the current is 12 amperes when the resistance is 240 ohms, what is the current when the resistance is 540 ohms?
240 / 12 = x / 540
To find the current when the resistance is 540 ohms, we can use the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases proportionally.
In this case, the current (I) and the resistance (R) are inversely proportional. Mathematically, we can express this relationship as I = k/R, where k is a constant.
To find the value of k, we can use the given information that the current is 12 amperes when the resistance is 240 ohms. Substituting these values into the equation, we have:
12 = k/240
To solve for k, we can cross-multiply and solve for k:
12 * 240 = k
k = 2880
Now that we have the value of k, we can find the current (I) when the resistance (R) is 540 ohms. Plugging in these values into the equation, we have:
I = k/R
I = 2880/540
Simplifying the expression, we get:
I = 5.333 amperes
Therefore, when the resistance is 540 ohms, the current will be approximately 5.333 amperes.