Change in potential energy across wires differing composition

[Mebmt]

1. Homework Statement

9 V battery is connected to wire made up of three segments of different materials connected in a series: 10 cm copper, then 12 cm iron, then 18 cm tungsten. All wires are 0.26 mm diameter. Find potential difference across each wire.

Constants:
p Copper= 1.7 x 10-8
p Iron = 9.7 x 10 -8
p Tungsten = 5.6 x 10-8

26 mm diameter = 0.13 mm radius or 1.3 x 10-4 m

Homework Equations

R=pl/A

area of wire (1.3 x 10-4)(1.3 x 10-4) x pi = 5.31 x 10-8 meters squared

The Attempt at a Solution

Copper Resistance
R=pl/a
R= (1.7 x 10-8 ohm m)(.1m)/5.31 x 10-8 meters squared
R=0.032 ohm

Iron Resistance
R=pl/a
R=(9.7 x 10-8 ohm m)(.12m)/5.31 x 10-8 meters squared
R=0.22 ohm

Tungsten Resistance
R=pl/a
R=(5.6 x 10-8 ohm m)(0.18 m)/5.31 x 10-8 meters squared
R=0.19

R total series = r1 + r2 + r3
= .032 + .22 + .19
= 0.442 ohm


V copper = vtotal * Rcopper/R total
= 9 V * .032/.442
= 0.65 V

V silver = vtotal *Rsilver/R total
=9 V * .22/.442
=4.48 V

V Tungsten = vtotal * Rtungsten/R total
=9V *.387/.442
= 3.87 V

Volts all add up to 9 so 2nd Law is good but my answers are wrong somewhere...

Thanks,
Scott

 

[PeterO]

1. Homework Statement

9 V battery is connected to wire made up of three segments of different materials connected in a series: 10 cm copper, then 12 cm iron, then 18 cm tungsten. All wires are 0.26 mm diameter. Find potential difference across each wire.

Constants:
p Copper= 1.7 x 10-8
p Iron = 9.7 x 10 -8
p Tungsten = 5.6 x 10-8

26 mm diameter = 0.13 mm radius or 1.3 x 10-4 m

Homework Equations

R=pl/A

area of wire (1.3 x 10-4)(1.3 x 10-4) x pi = 5.31 x 10-8 meters squared

The Attempt at a Solution

Copper Resistance
R=pl/a
R= (1.7 x 10-8 ohm m)(.1m)/5.31 x 10-8 meters squared
R=0.032 ohm

Iron Resistance
R=pl/a
R=(9.7 x 10-8 ohm m)(.12m)/5.31 x 10-8 meters squared
R=0.22 ohm

Tungsten Resistance
R=pl/a
R=(5.6 x 10-8 ohm m)(0.18 m)/5.31 x 10-8 meters squared
R=0.19

R total series = r1 + r2 + r3
= .032 + .22 + .19
= 0.442 ohm


V copper = vtotal * Rcopper/R total
= 9 V * .032/.442
= 0.65 V

V silver = vtotal *Rsilver/R total
=9 V * .22/.442
=4.48 V

V Tungsten = vtotal * Rtungsten/R total
=9V *.387/.442
= 3.87 V

Volts all add up to 9 so 2nd Law is good but my answers are wrong somewhere...

Thanks,
Scott

I like your reasoning - and your answers - so check that you have transcribed the figures correctly, and looked at the correct answers in you book.

 

[Mebmt]

Thanks Peter. The prof had changed the numbers on the website from those provided in the book. I had overlooked one of them.

 

[PeterO]

Thanks Peter. The prof had changed the numbers on the website from those provided in the book. I had overlooked one of them.

Note: when I worked this out I ignored the diameter - since they were all the same, as well as the 10^-8 on each of the resistivities, [they all had the same factor] since I knew at the end I was only going use the resistances in the form of fractions - where those values would cancel anyway.

 

[asteriatic]

I would like to point out that the potential energy across wires differing in composition is a result of the different resistances of each material. This is due to the different properties of each material, such as their electrical conductivity and resistivity. The potential difference across each wire can be calculated using Ohm's Law, which states that the potential difference (V) is equal to the current (I) multiplied by the resistance (R). In this case, the current is the same throughout the series circuit, so the potential difference is directly proportional to the resistance of each wire.

Your approach in calculating the resistance of each wire is correct. However, the total resistance in a series circuit is not simply the sum of the individual resistances, but rather the sum of each resistance multiplied by the length of the wire. This is because the current must pass through each segment of wire, and the longer the wire, the higher the resistance. Therefore, the correct equation for the total resistance in this circuit would be:

R total = R copper * (10 cm/100 cm) + R iron * (12 cm/100 cm) + R tungsten * (18 cm/100 cm)

= 0.032 ohm + 0.22 ohm + 0.19 ohm

= 0.442 ohm

Using this value for the total resistance, we can then calculate the potential difference across each wire using Ohm's Law:

V copper = 9 V * (0.032 ohm / 0.442 ohm) = 0.65 V
V iron = 9 V * (0.22 ohm / 0.442 ohm) = 4.48 V
V tungsten = 9 V * (0.19 ohm / 0.442 ohm) = 3.87 V

As you can see, the total potential difference across all three wires adds up to 9 V, indicating that the second law of thermodynamics is satisfied. I would also like to note that the diameter of the wires is not relevant in this calculation, as the resistance is determined by the length and cross-sectional area of the wire.

In conclusion, the change in potential energy across wires differing in composition is due to the different resistances of each material, which can be calculated using Ohm's Law. The total resistance in a series circuit is not simply the sum of the individual resistances, but rather