in an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 5A, the resistance is 20 ohms. What is the current when the resistance is 25 OHMs?
first set up a regular proportion:
5a/x = 20 ohms/ 25 ohms
Because the problem says the current varies inversely you would flip only one side of the proportion:
5A/xA = 25 ohms/ 20 ohms
cross multiply:
100 = 25x ohms
Divide by 25:
x = 4A
I = k(1/R), where I current, R is resistance and k is a constant
given: I = 5, R = 20
5 = k(1/20)
k = 100
I = 100(1/R)
so when R = 25
I = 100(1/25) = 4
To solve this problem, we can use the concept of inverse variation.
Inverse variation is a relationship between two variables in which one variable increases while the other variable decreases at a constant rate.
In this problem, we know that the current passing through a conductor varies inversely with the resistance. This means that as the resistance increases, the current decreases, and vice versa.
Let's denote the current as I and the resistance as R. According to the problem, when the current is 5A, the resistance is 20 ohms.
Using inverse variation, we can write the equation as:
I ∝ 1/R
To find the constant of proportionality, k, we can substitute the given values into the equation:
5A ∝ 1/20Ω
To isolate k, we multiply both sides of the equation by 20Ω:
5A * 20Ω = 1
100Ω * A = 1
Now, we can solve for A, which represents the current when the resistance is 25 ohms.
25Ω * A = 1
Dividing both sides of the equation by 25Ω:
A = 1/25Ω
Therefore, the current when the resistance is 25 ohms is 1/25 A, or 0.04 A (rounded to two decimal places).
So, the current is 0.04A when the resistance is 25 ohms.