In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is
2 A
(amperes), the resistance is
100
ohms. What is the resistance when the current is
25 A
?
We can use the inverse variation formula:
current x resistance = constant
Let's call the constant k:
2 x 100 = k
k = 200
Now, we can use the same formula and the value of k to solve for the new resistance:
25 x resistance = 200
resistance = 8 ohms
Therefore, when the current is 25 A, the resistance is 8 ohms.
To solve this problem, we can use the formula for inverse variation:
k = current × resistance
where k is a constant.
First, we can find the value of k using the initial values given:
k = 2 A × 100 ohms = 200
Now, we can use this value of k to determine the resistance when the current is 25 A:
25 A = 200 / resistance
To isolate the resistance, we can rearrange the equation:
resistance = 200 / 25 A
Evaluating this expression:
resistance = 8 ohms
Therefore, when the current is 25 A, the resistance is 8 ohms.