How Many Electrons Pass Through a Gold Wire Per Second?

In summary, the resistivity of gold is 2.44 x 10^-8 Ω m at 20°C. Using this and the given current of 380 mA, the number of electrons per second passing through the wire can be approximated by using the fact that 6.241 x 10^18 electrons/sec pass through a circuit with a current of 1 A. This results in a closest answer of A) 2.4 x 10^18. The other information given in the problem is irrelevant for solving this question.
  • #1
victorializ
20
0

Homework Statement



The resistivity of gold is 2.44 x 10-8 Ω m at a temperature of 20°C. A gold wire, 0.5 mm in diameter and 44 cm long, carries a current of 380 ma. The number of electrons per second passing a given cross section of the wire, is closest to:

A) 2.4 × 10^18
B) 1.2 × 10^22
C) 2.8 × 10^14
D) 2.4 × 10^17
E) 6.3 × 10^15

Homework Equations



R=ρL/A

The Attempt at a Solution



R=(2.44 x 10^-8) (.44)/∏(.00025^2)
R= .0547
then i multiplied the resistance by the current (.38) to get .021 for a voltage.
then i divided that by (1.6 x 10^-19) and got 1.3 x 10^17 which isn't right but is close to the answer which is A
 
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  • #2
Why did you divide a voltage by the electron charge? Do you expect the right unit "per second" as result of that calculation?

You are given the current. What does a current of 1 A (example value) mean?
 
  • #3
victorializ said:

Homework Statement



The resistivity of gold is 2.44 x 10-8 Ω m at a temperature of 20°C. A gold wire, 0.5 mm in diameter and 44 cm long, carries a current of 380 ma. The number of electrons per second passing a given cross section of the wire, is closest to:

A) 2.4 × 10^18
B) 1.2 × 10^22
C) 2.8 × 10^14
D) 2.4 × 10^17
E) 6.3 × 10^15

Homework Equations



R=ρL/A

The Attempt at a Solution



R=(2.44 x 10^-8) (.44)/∏(.00025^2)
R= .0547
then i multiplied the resistance by the current (.38) to get .021 for a voltage.
then i divided that by (1.6 x 10^-19) and got 1.3 x 10^17 which isn't right but is close to the answer which is A

Something's off by a factor of 18.5 and you call that 'close'?

Learn that people are going to give you problems with a lot of irrelevant information!
 
  • #4
mfb said:
Why did you divide a voltage by the electron charge? Do you expect the right unit "per second" as result of that calculation?

You are given the current. What does a current of 1 A (example value) mean?

so i need to use the fact that 6.241 x 10^18 electrons/sec pass through a circuit which is 1 A 

when i use that number though i still have it wrong so I'm not really sure where else my calculations are messed up.
 
  • #5
victorializ said:
so i need to use the fact that 6.241 x 10^18 electrons/sec pass through a circuit which is 1 A 

when i use that number though i still have it wrong so I'm not really sure where else my calculations are messed up.

But the current isn't 1 A.
 
  • #6
dauto said:
But the current isn't 1 A.

oh my goodness so most of the information in this problem is irrelevant? all i need is to do a proportion between 1A and the 38 mA in the problem?
 
  • #7
victorializ said:
oh my goodness so most of the information in this problem is irrelevant? all i need is to do a proportion between 1A and the 38 mA in the problem?
If that gets you closer to the right answer, go for it! :smile:

380 mA would be even better ... :wink:
 
  • #8
victorializ said:
oh my goodness so most of the information in this problem is irrelevant? all i need is to do a proportion between 1A and the 38 mA in the problem?
Yes (apart from the typo (?) NascentOxygen pointed out).
 

Related to How Many Electrons Pass Through a Gold Wire Per Second?

1. What is the relationship between resistance and current in a wire?

The relationship between resistance and current in a wire is described by Ohm's Law, which states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. This means that as resistance increases, current decreases, and vice versa.

2. How does the length of a wire affect resistance?

The length of a wire has a direct effect on its resistance. As the length of the wire increases, the resistance also increases. This is because longer wires offer more resistance to the flow of electrons compared to shorter wires.

3. What is the unit of measurement for resistance?

The unit of measurement for resistance is Ohm (Ω). This unit is named after the German physicist Georg Ohm, who first described the relationship between voltage, current, and resistance in a circuit.

4. How does the material of a wire affect resistance?

The material of a wire can greatly affect its resistance. Materials with high electrical conductivity, such as copper, have low resistance, while materials with low electrical conductivity, such as rubber, have high resistance. This is due to the ease with which electrons can flow through the material.

5. What is the difference between resistance and impedance?

Resistance and impedance are often used interchangeably, but they have different meanings. Resistance is the opposition to the flow of electrons in a wire, while impedance includes both resistance and reactance (the opposition to the flow of alternating current). In simpler terms, resistance only applies to direct current, while impedance applies to both direct and alternating current.

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