Electric current and resistance question

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SUMMARY

The discussion focuses on calculating the cross-sectional area of a combined copper and nichrome wire with a total resistance of 10 kΩ. The copper wire measures 8 inches and the nichrome wire measures 10 inches, with the nichrome wire having twice the cross-sectional area of the copper wire. Key equations include the resistance formula R = ρ × (l/A) and the resistivity values of copper (1.7 x 10^-8 Ω·m) and nichrome (150 x 10^-8 Ω·m). The solution requires applying these equations to find the areas of both wires.

PREREQUISITES
  • Understanding of electrical resistance and Ohm's Law (I = V/R)
  • Familiarity with resistivity concepts and units (Ω·m)
  • Knowledge of how to manipulate algebraic equations
  • Basic understanding of wire materials and their properties (copper and nichrome)
NEXT STEPS
  • Study the derivation and application of the resistance formula R = ρ × (l/A)
  • Learn about the temperature coefficient of resistance and its implications
  • Explore the properties of different conductive materials, focusing on resistivity
  • Practice solving problems involving series and parallel resistances in circuits
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Students studying electrical engineering, physics enthusiasts, and anyone interested in practical applications of resistance and material properties in electrical circuits.

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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Likes   Reactions: berkeman
@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.
 

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