Inverse proportionality

[johnkivan]

Strategy Guide - Eq., Ineq & VICs
Edition - 4th
Chapter - 5
Page No. - 76

Q. The amount of electrical current that flows through a wire is inversly proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many amperers of electrical current will flow through the wire?

Ans. Using 3 as the original resistance and 1 as the new resistance, we can see that the new electrical current will be 12 amperes.

C1 * R1 = C2 * R2
4 * 3 = C2 * 1
12 = C2

Query:
In the question it is said that "The amount of electrical current that flows through a wire is inversly proportional to the resistance in that wire". Therefore, shouldn't C1 and R1 have an inverse relationship? Please explain how we can take "3" as a smart number to solve this problem.

[ps63739]

If any value is inversly proportional (or proportional) then you can add a constant and equate the euation.

Say x is proportional to y. So x=Ky (where K is a constant.) And for any value of x and y x/y will be constant.

Similarly here
You can say C (inversly proportional to R or proportional to 1/R)
So C = K/R, so C*R will be constant. For any value of C and R.

That's the equation you have used here.

[Ben Ku]

Query:
In the question it is said that "The amount of electrical current that flows through a wire is inversly proportional to the resistance in that wire". Therefore, shouldn't C1 and R1 have an inverse relationship? Please explain how we can take "3" as a smart number to solve this problem.

Inverse relationship means that as one increases, the other decreases. Mathematically, this means the product of the two variables is constant:

xy = k, if x and y are inversely related.

Logically, if you cut the resistance by 1/3, then the current will increase 3 times. The resistance decreases, the current increases.