How to Calculate Current in a Coated Tube Connected to a Battery?

In summary: Just remember to include the units in your final answer. In summary, a plastic tube coated with a layer of silver 0.100 mm thick and connected to a 12.0-V battery will have a current of 410.2 A flowing through it, with the resistance of the coated tube being 0.02952 ohms.
  • #1
Soaring Crane
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Homework Statement



A plastic tube 25.0 m long and 4.00 cm in diameter is dipped into a silver solution, depositing a layer of silver 0.100 mm thick uniformly over the outer surface of the tube. If this coated tube is then connected across a 12.0-V battery, what will be the current?

Homework Equations



R = (p*L)/A

V = I*R, where I = V/R


The Attempt at a Solution



I’m a bit uncertain about this problem since there is both a semiconductor (Ag) and plastic involved.

A = 2*pi*(r1 + r2)*L – 2*pi*(r1)*L = 2*pi*r2* L = 2*pi*(0.100* 10^-3 m)*25 m = 0.0157 m^2?

R = (p_Ag*L)/A = [(1.47*10^-8 ohm*m)*(25 m)]/(0.0157 m^2) = 2.34*10^-5 ohm?

I = 12 V/(2.34*10^-5 m^2 ohm) = 5.129*10^5 A ?

If the above is incorrect, please direct me. Any help is appreciated.

Thanks.
 
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  • #2
1) Ag is not a semiconductor - it's a conductor. I would assume the plastic is an insulator.

2) A is the cross-sectional area of the silver coating. It doesn't involve L. I would rethink that part of the calculation.

3) The units for R are just ohms. Take another look at that line.
 
  • #3
A = pi*(d + r)^2 - pi*r^2, where r is radius of insulator section and d is thickness of Ag layer

A = pi*[0.02 m + (0.1*10^-3 m)] - pi(0.02 m)^2
= 0.001269 m^2 - 0.001257 m^2
= 1.256*10^-5 m^2

R = [25 m*(1.47*10^-8 ohm*m)]/[1.256*10^5 m^2]
= 0.02952 ohm

I = (12 V)/(0.02952 ohm) = 410.2 A ?
 
  • #4
Looks good to me!
 

What is a current and painted tube?

A current and painted tube is a type of tube used in scientific experiments to create an electrical current. It is made of a conductive material, such as copper or aluminum, and is coated with a layer of paint to prevent electrical interference.

How is a current and painted tube used in experiments?

A current and painted tube is used to create a controlled electrical current in an experiment. By adjusting the voltage and position of the tube, scientists can study the effects of electricity on various materials or organisms.

What are the benefits of using a current and painted tube?

One benefit of using a current and painted tube is that it allows for precise control of the electrical current in an experiment. The painted coating also helps to reduce any unwanted electrical interference, ensuring accurate results.

Are there any limitations to using a current and painted tube?

One limitation of using a current and painted tube is that it can only produce a relatively low amount of current. This may not be sufficient for certain experiments that require a higher voltage or current.

Can a current and painted tube be used in other applications besides scientific experiments?

Yes, a current and painted tube can be used in various industries, such as electronics and telecommunications. They are also commonly used in household appliances and electrical wiring systems.

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