How to Calculate Current in a Silver-Lined Tube?

[Feldoh]

Homework Statement

A plastic tube 25m long and 4cm in diameter is dipped into a silver solution, resulting in a layer of silver being deposited 0.1mm think uniformly over the outer surface of the plastic tube. The coated tube is then connected across a 12V battery. Calculate the current.

Homework Equations

Current/Resistance equations that are time invariant

The Attempt at a Solution

I THINK that I need to find the current density in order to solve this problem, however I cannot think of a way to find it. I also thought about some way to do this by finding the resistance but you need the resistivity of silver. I could look on line but the value isn't provided in my book or in the homework set so I thinking that I'm not supposed to just look-up the resistivity of silver.

 

[berkeman]

I would just look up the resistivity of silver, calculate the resistance of that geometry, and use that to calculate the current. Don't worry that the book doesn't give you the rho of silver -- it's common to look up resistivities of materials in a CRC handbook or nowadays just online.

 

[baba89]

I would suggest approaching this problem by first considering the properties of silver and its behavior in an electrical circuit. Silver is a highly conductive metal and is often used in electrical wiring and components. In order to calculate the current in this circuit, we need to take into account the resistivity of silver and the length and cross-sectional area of the coated tube.

To find the resistivity of silver, we can refer to reliable sources such as a physics reference book or online database. The resistivity of silver is approximately 1.59 x 10^-8 ohm-meters. From this value, we can calculate the resistance of the coated tube using the formula R = ρ * (L/A), where ρ is the resistivity, L is the length of the tube, and A is the cross-sectional area.

Next, we can use Ohm's Law (I = V/R) to calculate the current in the circuit, where V is the voltage of the battery and R is the resistance of the coated tube that we calculated earlier. Plugging in the given values (V = 12V, R = calculated resistance), we can determine the current in the silver-lined tube.

In conclusion, by considering the properties of silver and using equations such as Ohm's Law and the formula for resistance, we can calculate the current in a silver-lined tube connected to a 12V battery. It is important to use reliable sources for the properties of materials in scientific calculations, rather than simply looking them up online.