Question

in an electric circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 5A (amperes), the resistance is 44 ohms. What is the resistance when the current is 2A

Answer 1

Current is 5A
Resistance is 44 ohms
(sorry)

Answer 2

Find voltage from first set of data and then use it to calculate resistance afterwards

Answer 3

Direct variation: \(y = kx\)

Inverse variation: \(y = \dfrac{k}{x} \)

Use the given info to find k.

Then write \(y = \dfrac{k}{x} \) with the correct value of k you found.

Then enter x and find y.

Answer 4

Ahh yes... That is proper mathematical modeling way (y) @mathstudent55

Answer 5

@mathstudent55 what do I substitute in for y and k?

Answer 6

Current and resistance are inversely related.
Therefore, current = k / resistance ---- (1)
We are given that when resistance = 44 ohms, current = 5 A
Substitute in (1): 5 = k / 44
k = 5 * 44 = 220
Put k = 220 in (1)
current = 220 / resistance ---- (2)

What is the resistance when the current is 2A?
Put current = 2 in equation (2) and find resistance:
2 = 220 / resistance
2 * resistance = 220
resistance = 220 / 2 = 110 ohms.

Answer 7

A quicker way to do this problem follows:
Since current and resistance are inversely related it implies that as current decreases from 5A to 2A, which is a factor of 2/5, the resistance will increase by a factor of 5/2 (because of inverse relation).
Therefore, new resistance = 5/2 * old resistance = 5/2 * 44 = 5 * 22 = 110 ohms.

Answer 8

Thank you all!

Answer 9

You are welcome.