# Finding Resistance and Inductance of solenoid

1. May 21, 2005

### 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

Last edited: May 21, 2005
2. May 21, 2005

### 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.

Last edited: May 21, 2005
3. May 21, 2005

### 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?

Last edited: May 21, 2005
4. May 21, 2005

### OlderDan

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