Comparing Current in two different wires

In summary, wire A and wire B, made of different metals, are subjected to the same electric field in two different circuits. Wire B has 5 times the cross-sectional area, 1.1 times as many mobile electrons per cubic centimeter, and 2 times the mobility of wire A. In the steady state, 2E18 electrons enter wire A every second. By using the equation i = nAuE, it can be determined that 2.2E25 electrons enter wire B every second.
  • #1
aba3
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Problem:
Suppose wire A and wire B are made of different metals, and are subjected to the same electric field in two different circuits. Wire B has 5 times the cross-sectional area, 1.1 times as many mobile electrons per cubic centimeter, and 2 times the mobility of wire A. In the steady state, 2E18 electrons enter wire A every second. How many electrons enter wire B every second?

Equation:
i = nAuE
n = Electrons/cubic meter
A = cross-sectional area
u = mobility of electrons
E = electric fieldSolution:
ib=ia * 2*5*1.1E6
it is 1.1E6 because the mobility factor needs to be in electrons/ cubic meter

ib = 2.2E25

Webassign says that's wrong. I can't come up with anything else
 
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  • #2
ib=ia * 2*5*1.1E6
Omit the E6. The whole story is
i = nAuE = 2*n1*5*A1*1.1*u1*E
= 2*5*1.1*n1*A1*u1*E
= 2*5*1.1*i1
= 2*5*1.1*2E18
If 1.1 times as many electrons per cm^3, then there will be 1.1 times as many electrons per m^3 too.
 
  • #3
there are a million cubic centimeters in a meter cube. if each cubic cm has 1.1 more electron then the meter cube has 1.1E6 extra electrions
(Also, I already tried that and webassign said I was wrong).
 
  • #4
No. It doesn't give a count of the extra electrons. It says the other wire has 10% more per cm^3. That means 10% more per m^3. Say the first one has 100 per cm^3. Then the second will have 110.
Per m^3 the first one will have 100*1E6 and the second will have
110*1E6. The ratio will be 110E6/100E6 = 1.1Kind of like saying what if every student in the class overeats and comes back to class on Monday 10% heavier. Then the whole class together will be 10% heavier, not 10*the number of students heavier in pounds, kg or tons.
 
  • #5
You were right. Thanks.
 

1. What factors can affect the current in two different wires?

The current in two different wires can be affected by factors such as the wire's resistance, length, and cross-sectional area. Other factors include the type of material the wire is made of, temperature, and the voltage applied to the circuit.

2. How do you compare the current in two different wires?

The most common way to compare the current in two different wires is by using Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R). By measuring the voltage and resistance of each wire, you can calculate and compare the current flowing through them.

3. Can two wires with the same resistance have different currents?

Yes, two wires with the same resistance can have different currents if they have different voltages applied to them. According to Ohm's law, the current is directly proportional to the voltage, so a higher voltage will result in a higher current even if the resistance is the same.

4. How does the length of a wire affect the current?

The length of a wire has a direct effect on its resistance, which in turn affects the current. A longer wire will have a higher resistance, meaning a lower current will flow through it. This is due to the increased distance the electrons have to travel, resulting in more collisions and a slower flow of current.

5. Can the cross-sectional area of a wire affect the current?

Yes, the cross-sectional area of a wire can affect the current. A wire with a larger cross-sectional area will have lower resistance, allowing more current to flow through it. This is because a larger area provides more space for the electrons to move through, reducing the number of collisions and increasing the flow of current.

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