Calculating Current Density & Current in Gold Wire

In summary, current density can be calculated by dividing the current flowing through a section of gold wire by the cross-sectional area of the wire. It is measured in amperes per square meter (A/m²). Current in gold wire can be determined using Ohm's law and the wire's length, cross-sectional area, and resistivity. The current density in gold wire affects its resistance, with higher current densities leading to an increase in resistance. To determine the thickness of gold wire, you can use the equation R=ρL/A and solve for A to calculate the cross-sectional area and determine the wire's thickness based on its shape.
  • #1
kyang002
22
0
The electron drift speed in a gold wire is 3.0 * 10^-4.

1. What is the current density in the wire?

2. What is the current if the wire diameter is 0.50 mm?

I am unsure of which equation to use.
Q = I delta t ??

Can someone help me out?
 
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  • #2
Is it too hard to post all your questions in one thread?

Also, how on Earth does Q = I delta t help you? How about I = nAqv?
 
  • #3


To calculate the current density in the wire, we can use the equation J = I/A, where J is the current density, I is the current, and A is the cross-sectional area of the wire. Since we are given the electron drift speed (v) in the wire, we can use the equation I = nqvA, where n is the number of free electrons per unit volume, q is the charge of an electron, and A is the cross-sectional area of the wire.

1. Using the given electron drift speed of 3.0 * 10^-4, we can calculate the current density as follows:

J = I/A = (nqvA)/A = nqv

Since we do not have information about the number of free electrons per unit volume, we cannot calculate the exact value of current density. However, we can say that the current density in the gold wire will be directly proportional to the electron drift speed.

2. To calculate the current in the wire, we can use the equation I = nqvA, where n is the number of free electrons per unit volume, q is the charge of an electron, v is the electron drift speed, and A is the cross-sectional area of the wire.

Since we are given the wire diameter, we can calculate the cross-sectional area using the formula A = πr^2, where r is the radius of the wire.

r = 0.50 mm/2 = 0.25 mm = 0.25 * 10^-3 m

A = π(0.25 * 10^-3)^2 = 1.96 * 10^-7 m^2

Now, we need to find the number of free electrons per unit volume (n) in gold. This value can be found in a table of material properties or can be calculated using the density of gold (19.3 g/cm^3) and its atomic mass (196.97 g/mol).

n = (density * Avogadro's number)/atomic mass = (19.3 g/cm^3 * 6.022 * 10^23 mol^-1)/196.97 g/mol = 5.92 * 10^28 electrons/m^3

Substituting the values in the equation I = nqvA, we get:

I = (5.92 * 10^28 electrons/m^3) * (1.6 *
 

1. How do you calculate current density in gold wire?

Current density is calculated by dividing the current flowing through a section of gold wire by the cross-sectional area of that wire. The formula is J=I/A, where J is current density in amperes per square meter, I is current in amps, and A is the cross-sectional area in square meters.

2. What is the unit of measurement for current density?

Current density is measured in amperes per square meter (A/m²).

3. How is current calculated in gold wire?

Current can be calculated using Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R). In the case of gold wire, the resistance can be calculated using the wire's length, cross-sectional area, and resistivity (ρ). The formula is I=V/(ρL/A), where I is current in amps, V is voltage in volts, ρ is resistivity in ohm-meters, L is wire length in meters, and A is cross-sectional area in square meters.

4. How does the current density in gold wire affect its resistance?

Current density plays a role in determining the resistance of gold wire. As the current density increases, the resistance also increases. This is because higher current densities cause more collisions between electrons and gold atoms, leading to an increase in resistance.

5. How do you use current density and current to determine the thickness of gold wire?

To determine the thickness of gold wire, you can use the equation R=ρL/A, where R is resistance, ρ is resistivity, L is wire length, and A is cross-sectional area. By rearranging the equation to solve for A, you can calculate the cross-sectional area of the wire. From there, you can determine the wire's thickness based on its shape (e.g. circular wire's thickness = diameter).

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