Finding Resistance and Inductance of solenoid

[teknodude]

The inductance of the solenoid determines the time it takes to establish this current. Find the inductance,the resistance, and the time constant of a solenoid that is constructed by wrapping five “tightly wound” (i.e., wire-against-wire like this ) layers of 0.30 mm diameter copper wire on a toilet paper roll that is 11.5 cm long and 4.3 cm in diameter. (The resistivity of copper is 1.7 x 10^8 ohm-meter. Hint: Find the number of “turns” in the solenoid. You may assume that the diameter of each turn is 4.3 cm.)

radius of copper wire= 1.5x10^-4 m
radius of toilet paper roll= 0.0215m
length of TP roll= 0.115m

I'm thinking that i need to find resistance first, but what's confusing me is that the toilet paper roll is being wrapped by layers of copper wire. So I might have to take into account of the added thickness of the toilet paper roll.
I know I have to use the following equation:
$$R=\frac{\rho L} {A}$$ rho is the resistivity, A=cross sectional area, L=length

The hint says to find the number of “turns” in the solenoid. I'm thinking that in order to find the # of turns is to take the given length and divide by the circumferance of the TP roll.
$$# of turns=\frac{0.115} {2\pi*1.5*10^-4}$$
But then how do i find the length of the copper wire?


I know the answer for the resistance is 62.3 ohms. I tried working backwards and found that the L=259meters. I can't seem to get that length... what i am i doing wrong

 

[OlderDan]

The number of turns will be the length of the roll divided by the diameter of the wire times 5 for the 5 layers. The length of each turn is one circumference of the roll.

 

[teknodude]

Thank you olderdan

Also for calculating the inductance, I am using this equation
$$L=\mu_0n^2V$$

n is the number of turns per unit length. Do i just divide the number of turns that i got from the first part by the length of the wire to get n?

 

[OlderDan]

Thank you olderdan

Also for calculating the inductance, I am using this equation
$$L=\mu_0n^2V$$

n is the number of turns per unit length. Do i just divide the number of turns that i got from the first part by the length of the wire to get n?

It is the number of terns per unit length of the solenoid, not per unit length of the wire.