How Does Changing Wire Dimensions Affect a Capacitor's Discharge Time Constant?

[denian]

capacitor --> time constant

i'm blur with this q.

a capacitor discharges through a resistor made of a length of wire. the time constant of the circuit is [tau1]. when the resistor is substituted with another wire made of the same metal but of twice the diameter and twice the length of the first wire, the time constant of the circuit is [tau2]
what is the ratio of [tau2] : [tau1]

the answer i get is 2 : 1
but the answer is 1 : 2

please explain the method i should use.

 

[HallsofIvy]

What method DID you use?

A good analogy for electricity through a wire is water through a pipe. If one pipe has a larger diameter than another will water go through it faster or slower? Will it take more or less time to empty a tank?

 

[Doc Al]

please explain the method i should use.

Two questions for you:
(1) How do you calculate the time constant of an RC (resistor-capacitor) circuit?
(2) How does resistance depend on diameter and length?

The more you show us of how you did it, the quicker we can help you.

 

[denian]

i was wrong.
the method i used is
[tau] is proportional to R
and R is directly proportional with length
so, that is why i get 2:1

i did not consider the diameter factor.

 

[Doc Al]

i did not consider the diameter factor.

And resistance is inversely proportional to diameter squared.

 

[denian]

thank you.
but can we actually prove that it is inversely proportional to ( diameter )^2 ?

 

[Doc Al]

but can we actually prove that it is inversely proportional to ( diameter )^2 ?

Not sure what you mean by "prove", but you should know the relationship between resistance and length, area, and resistivity (ρ, which depends on the material):
$$R = \frac{\rho l}{A}$$

 

[denian]

i haven't learn that.
thank you, doc al.