Electric current and resistance question

In summary, the problem involves finding the cross sectional area of an 8 inch copper wire and a 10 inch nichrome wire when their combined resistance is 10 kΩ. The nichrome wire has twice the area of the copper wire. To solve this, we can use the equation R = ρ * (l/A), where R is the resistance, ρ is the resistivity, l is the length of the conductor, and A is the cross sectional area. We can also use the formula R2 = R1 * (1 + α(T2 - T1)), where R2 is the resistance at temperature T2, R1 is the resistance at temperature T1, and α is the temperature coefficient. The resist
  • #1
Elisapan622
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Homework Statement
problem solving

You build a wire by combining an 8 inches copper wire with a 10 inches nichrome wire. If their combine resistance is 10 kΩ, find the cross section area of both wires. The nichrome wire has twice the area of the copper wire.
Relevant Equations
I = V/R

R=\rho \times \frac{l}{A}
R is the resistance in ohms (Ω).

ρ is the resistivity in ohms-meter (Ω×m)

l is the length of the conductor in meter (m)

A is the cross sectional area of the conductor in square meters (m2)

R2 = R1 × ( 1 + α(T2 - T1) )

R2 is the resistance at temperature T2 in ohms (Ω).

R1 is the resistance at temperature T1 in ohms (Ω).

α is the temperature coefficient.
Homework Statement:: problem solving

You build a wire by combining an 8 inches copper wire with a 10 inches nichrome wire. If their combine resistance is 10 kΩ, find the cross section area of both wires. The nichrome wire has twice the area of the copper wire.
Homework Equations:: I = V/R

R=\rho \times \frac{l}{A}
R is the resistance in ohms (Ω).

ρ is the resistivity in ohms-meter (Ω×m)

l is the length of the conductor in meter (m)

A is the cross sectional area of the conductor in square meters (m2)

R2 = R1 × ( 1 + α(T2 - T1) )

R2 is the resistance at temperature T2 in ohms (Ω).

R1 is the resistance at temperature T1 in ohms (Ω).

α is the temperature coefficient.

Resistance of nichrome is 150 x 10^-8
Resistance of copper is 1.7 x 10^-8
Problem : You build a wire by combining an 8 inches copper wire with a 10 inches nichrome wire. If their combine resistance is 10 kΩ, find the cross section area of both wires. The nichrome wire has twice the area of the copper wire.

Formulas
I = V/R

R=\rho \times \frac{l}{A}
R is the resistance in ohms (Ω).

ρ is the resistivity in ohms-meter (Ω×m)

l is the length of the conductor in meter (m)

A is the cross sectional area of the conductor in square meters (m2)

R2 = R1 × ( 1 + α(T2 - T1) )

R2 is the resistance at temperature T2 in ohms (Ω).

R1 is the resistance at temperature T1 in ohms (Ω).

α is the temperature coefficient.
 
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  • #2
Show your work!
 
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  • #3
@Elisapan622 -- you are doing much better now posting in the schoolwork forums and posting the equations, thank you. Now you need to start writing the equations that you think you should use to solve this question. Please write the equation for the total resistance based on the sizes and lengths of the two wire pieces, and the resistivity of each material.

That will get you a lot closer to the solution. Thank you.
 

1. What is electric current and how is it measured?

Electric current is the flow of electric charge through a conducting material. It is measured in units of amperes (A).

2. What factors affect the flow of electric current?

The flow of electric current is affected by the voltage or potential difference, the resistance of the material, and the length and cross-sectional area of the material.

3. What is resistance and how is it related to electric current?

Resistance is the measure of how difficult it is for electric current to flow through a material. It is directly proportional to the voltage and inversely proportional to the current, meaning as resistance increases, current decreases.

4. How can resistance be reduced?

Resistance can be reduced by increasing the cross-sectional area of the material, decreasing the length of the material, or using a material with lower resistivity. Additionally, using thicker wires and keeping them clean and free of corrosion can also reduce resistance.

5. What is Ohm's law and how is it used in relation to electric current and resistance?

Ohm's law states that the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. This can be represented by the equation I = V/R, where I is current, V is voltage, and R is resistance. Ohm's law is used to calculate the amount of current flowing through a material given the voltage and resistance, or to calculate the resistance of a material given the voltage and current.

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