Question

The electrical resistance of a wire varies directly as the square of the diameter . if a wire 9.45m long and 0.09 cm in diameter has a resistance of a wire of the same material which is 15.5m in length and 0.16cm in diameter?

Answer 1

This goes in the physics portion :)

Answer 2

so sorry ... actually its my first time here ... and ive got a lots of papers to pass this week :((

Answer 3

No worries c:

Just close this up and post it in the physics portion :)

Answer 4

This is a standard direct variation problem. Such problems are encountered often in algebra, not just physics.

resistance varies directly as the square of the diameter MEANS

\(Resistance = k\cdot Diameter^{2}\)

We are given: wire 9.45m long and 0.09 cm in diameter has a resistance of a wire of the same material which is 15.5m in length and 0.16cm in diameter?

This is a little odd for two reasons:
1) the length is not important. Throw it out.
2) We have two partial hints and no complete hint.

Discarding the length will be more clear.

We are given: wire 0.09 cm in diameter has a resistance of a wire of the same material which is 0.16cm in diameter?

Thus: \(k\cdot (0.09\;cm)^{2} = k\cdot (0.16\;cm)^{2}\)

We see immediately that this is no good, since k = 0 is the only solution. I have to believe we DID need the length and the variation description provided is incorrect.

I would guess that it is this: The resistance of a wire varies directly with its length and inversely with the square of its diameter

Now, we can solve it with the original information given, Let's see what you get.

@conehate0712