# Calculating Current in a Wire of Given Dimensions

• Johnahh
In summary, the conversation discusses a wire with a current of 3.2A and a radius of 1.2mm, made of a material with 2.5x10^25 free electrons per cubic metre. After solving using the formula I=Anev and cross-sectional area = pi*r^2, it is determined that the electron drift velocity is 0.177 m/s. However, the given electron concentration for the wire is unusually low for a metal and should be in the range of 10^28-10^29 electrons/m^3. It is also noted that there was a typo in the cross-sectional area calculation, which does not affect the final answer. In regards to the question of what happens if
Johnahh

## Homework Statement

a wire carrying a current of 3.2A has a radius of 1.2mm. the material of the wire has 2.5x10^25 free electrons per cubic metre. the elementary charge is 1.6x10^-19

## Homework Equations

I=Anev
cross section = pi*r^2

## The Attempt at a Solution

pi*0.0012^2 = 4.5x10^6

3.2/4.5x10^6*2.5x10^25*1.16x10^-19 = 0.1777 recurring
I am sure this is not correct as it seems to fast, I have seen some examples and they are more like 2.8x10^-4 m/s
Am i supposed to make 2.5x10^25 into 2.5x10^19 for mm^3 instead of m^3?

2.5 x10^25 electrons per cubic metre is very low value for a metal wire. It should be in the range 10^28-10^29 electron/m^3.

ehild

you have the cross sec area as 4.5x10^6 ...it should be 4.5x10^-6... this is just a typing error and does not affect your answer.
For the figures you have given I also get 0.177
I agree with ehild regarding electron concentration for a metal. 10^28 to 10^29

Yeah it was a typo sorry. OK so the electron drift is 0.177 m/s. What happens if the cross section doubles in size is it v*2 or v/2? Thanks

I would like to clarify that the given problem statement does not provide enough information to accurately calculate the current in the wire. The formula for current, I = Anev, requires the cross-sectional area of the wire (A), the number of free electrons per unit volume (n), and the drift velocity (v). However, the problem statement only provides the radius of the wire and the number of free electrons per cubic meter, which does not give us enough information to calculate the cross-sectional area or the drift velocity.

In order to accurately solve this problem, we would need to know the length of the wire and the material it is made of, which would allow us to calculate the cross-sectional area. We would also need to know the temperature of the wire, as this affects the drift velocity of the free electrons.

Assuming we have all the necessary information, the correct approach to solving this problem would be to first convert the radius from millimeters to meters (since the free electrons per cubic meter is given) and then calculate the cross-sectional area using the formula A = πr^2. Next, we can calculate the drift velocity using the formula v = I/(Ane). Finally, we can plug in all the values to the formula I = Anev to calculate the current in the wire.

In conclusion, as a scientist, I would suggest providing all the necessary information in order to accurately solve this problem and avoid any confusion or incorrect calculations.

## 1. What is the formula for calculating current in a wire?

The formula for calculating current in a wire is I = V/R, where I is the current in amperes (A), V is the voltage in volts (V), and R is the resistance in ohms (Ω).

## 2. How do you calculate the resistance of a wire?

The resistance of a wire can be calculated using the formula R = ρL/A, where R is the resistance in ohms (Ω), ρ (rho) is the resistivity of the material in ohm-meters (Ωm), L is the length of the wire in meters (m), and A is the cross-sectional area of the wire in square meters (m²).

## 3. What is the unit of measurement for current?

The unit of measurement for current is amperes (A). One ampere is equal to one coulomb (C) of charge flowing through a conductor in one second.

## 4. How does the diameter of a wire affect the current?

The diameter of a wire does not directly affect the current. However, it can indirectly affect the current by changing the wire's resistance. A thicker wire has a lower resistance, allowing more current to flow through it compared to a thinner wire with a higher resistance.

## 5. Can current flow through an insulator?

No, current cannot flow through an insulator. Insulators have a high resistance to the flow of electricity, so they do not allow current to pass through them easily. This is why insulators are commonly used to protect wires and prevent electrical shocks.

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