Find current flowing through the wire

In summary: Just be sure to keep track of your units and make sure they are consistent. Good luck on your final try!In summary, the problem is solved by first finding the total resistance of the composite wire using the formula R = rho*L/(pi*r^2), where L is the length of each piece of wire and rho is the resistivity of the material. Then, the current can be calculated using the equation I = V/R. After correcting for a few errors, the final answer is 56.009737 A.
  • #1
Sean1218
86
0

Homework Statement



A wire of total length 34.00 m, consists of equal lengths of Cu followed by Al, both having the same diameter of 0.80 mm. A voltage difference of 86.0 V is placed across the composite wire. What is the current flowing in the wire? Use rho=1.72x10-8 ohm-m for the resistivity of copper and rho=2.82x10-8 ohm-m for the resistivity of aluminum.

Homework Equations



RT = RCu + RAl
R = rho*L/(pi*r2)
R = V/I

The Attempt at a Solution



Solve R = rho*L/(pi*r2) for both Cu and Al and add together for RT

(34*1.72*10^(-8))/(pi*.04^2) + (34*2.82*10^(-8))/(pi*.04^2)
= 0.000307089463

I = V/RT

86/0.000307089463
= 280048.684 ohm

Keep getting the wrong answer, what am I doing wrong?
 
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  • #2
Three things:

(1) If the total length is 34m, and it is made up of two pieces of equal length, how long is each piece?

(2) How many meters is 0.4mm?

(3) What are the units of current?
 
  • #3
Writing ohm was just a typo (was entering A before) and for some reason I was reading .80 mm as 80 mm, so I converted 80 mm -> .08 m. Completely forgot about halving the length though, thanks.

(17*1.72*10^(-8))/(pi*.0004^2) + (17*2.82*10^(-8))/(pi*.0004^2)
= 1.53544731

86/1.53544731
= 56.009737 A

That right then? I have one try left to get it right :s
 
  • #4
That looks right to me.
 
  • #5


I can confirm that your calculations are correct. However, the issue may lie in the units you are using. The resistivity values for copper and aluminum are given in ohm-meters, so your final answer should be in amperes (A) rather than ohms (Ω). To convert, you can use Ohm's Law (V=IR) to solve for current (I) by dividing the voltage (V) by the total resistance (RT). This gives a final answer of 0.000307 A or 307 microamps (μA). This means that the current flowing through the wire is very small due to the high resistivity of the materials used.
 

1. What is current?

Current is the flow of electric charge through a conductor, such as a wire.

2. How is current measured?

Current is measured in units of amperes (A) using a device called an ammeter. It measures the amount of charge passing through a given point in a circuit per unit of time.

3. What factors affect the amount of current flowing through a wire?

The amount of current flowing through a wire is affected by the voltage applied, the resistance of the wire, and the temperature of the wire.

4. How can I calculate the current flowing through a wire?

The current flowing through a wire can be calculated using Ohm's Law, which states that current (I) equals voltage (V) divided by resistance (R): I = V/R. This formula can also be rearranged to calculate voltage or resistance if the other two values are known.

5. What are some common applications of measuring current flowing through a wire?

Measuring current flowing through a wire is used in various applications, such as monitoring electricity usage, testing the health of electrical circuits, and controlling the flow of electricity in electronic devices.

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