Finding Resistance and Inductance of solenoid

• teknodude
In summary, the inductance of a solenoid is determined by the number of turns per unit length, which can be calculated by dividing the length of the solenoid by the diameter of the wire times the number of layers. The resistance of the solenoid can be found by using the equation R=\frac{\rho L} {A}, where \rho is the resistivity of copper, L is the length of the solenoid, and A is the cross-sectional area. The time constant can be found by using the equation L=\mu_0n^2V, where \mu_0 is the permeability of free space, n is the number of turns per unit length of the 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

Last edited:
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:
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:
teknodude said:
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.

1. What is a solenoid?

A solenoid is a coil of wire that is used to create a magnetic field when an electric current is passed through it. It is typically cylindrical in shape and can be found in many electronic devices, such as motors, speakers, and relays.

2. How do you find the resistance of a solenoid?

To find the resistance of a solenoid, you can use Ohm's Law which states that resistance (R) is equal to voltage (V) divided by current (I). You will need to measure the voltage and current of the solenoid using a multimeter, and then use the equation R = V/I to calculate the resistance.

3. What factors affect the resistance of a solenoid?

The resistance of a solenoid is affected by the length of the wire, the number of turns in the coil, the material of the wire, and the cross-sectional area of the wire. A longer wire, more turns, and a smaller cross-sectional area will result in a higher resistance.

4. How do you find the inductance of a solenoid?

To find the inductance of a solenoid, you can use the formula L = μn²A/l, where μ is the permeability of the material, n is the number of turns, A is the cross-sectional area, and l is the length of the solenoid. Alternatively, you can also use a special device called an inductance meter to measure the inductance directly.

5. Can the resistance and inductance of a solenoid be changed?

Yes, the resistance and inductance of a solenoid can be changed by altering the material of the wire, the number of turns, or the length and diameter of the solenoid. Additionally, the resistance and inductance of a solenoid can also be affected by the strength of the magnetic field it is placed in.

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