Current Electricity Homework: Rnet~l2/A & Variables

In summary, the conversation discusses the equations for resistance, current, and electric field in a circuit with various configurations. The main points are that the current and current density are constant in some cases, but the electric field and drift velocity are not. Additionally, the objects in parts C and D are not clearly defined and there is some confusion about the shape and configuration of the electrodes.
  • #1
zorro
1,384
0

Homework Statement



Refer figure

attachment.php?attachmentid=32966&stc=1&d=1299855441.jpg
Note: ~ stands for proportionality sign and p stands for resistivity.

The Attempt at a Solution



R=pl/A
Rnet~l2/A
V is constant across each conductor, so magnitude of electric field must be constant for every case. Since drift velocity depends on electric field, it is also constant for all. Wrong

Total current I in the circuit is constant in every case. But current density is constant only in A as area perpendicular to the current flow is constant. Correct.

Resistance per unit volume and Power dissipated per unit volume both are variables for all as both are functions of distance. Correct.

The only problem is with drift velocity and electric field.
 

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  • #2
Abdul Quadeer said:

Homework Statement



Refer figure

https://www.physicsforums.com/attachment.php?attachmentid=32966&stc=1&d=1299855441"


Note: ~ stands for proportionality sign and p stands for resistivity.

The Attempt at a Solution



R=pl/A
Rnet~l2/A
V is constant across each conductor, so magnitude of electric field must be constant for every case. Since drift velocity depends on electric field, it is also constant for all. Wrong

Total current I in the circuit is constant in every case. But current density is constant only in A as area perpendicular to the current flow is constant. Correct.

Resistance per unit volume and Power dissipated per unit volume both are variables for all as both are functions of distance. Correct.

The only problem is with drift velocity and electric field.

It's not too clear to me what the objects in C and D look like in three dimensions. Also, the configuration of the electrodes in C is not clear.

Use the differential form of your equation:

[tex]dR=\frac{\rho}{A}\,d\ell\,,[/tex]

then integrate.

Also, [tex]I=\int_S\vec{J}\cdot\vec{dA}\,,[/tex]

[tex]dV=-\vec{E}\cdot\vec{d\ell}[/tex]

and [tex]\vec{E}=\rho\vec{J}\,,[/tex]
 
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  • #3
I still don't get the answer.
Using your expressions, I got that E depends on x or r in every case i.e. it is not constant.
option (p) is included for (B) and (C) and option (s) for (A) only.
 
  • #4
It's still not clear to me: what objects are in C & D !

Spheres with spherical cavities? (Then how are they different? Is part of the electrode buried in C?)

Looking at the end of cylinders?

Ellipsoid with spherical cavity, or sphere with elliptical cavity.

Why is part of the wire going to the inside of C straight?
 
  • #5
This question now seems unclear to me too. Let's close this topic.
 

1. What is the formula for calculating current electricity using Rnet~l2/A?

The formula for calculating current electricity using Rnet~l2/A is I = Rnet~l2/A, where I represents the current in amperes (A), Rnet represents the net resistance in ohms (Ω), l represents the length of the conductor in meters (m), and A represents the cross-sectional area of the conductor in square meters (m2).

2. How do the variables Rnet, l, and A affect the current in the Rnet~l2/A formula?

The variable Rnet represents the net resistance of the conductor, which is a measure of how much the conductor resists the flow of electricity. The higher the resistance, the lower the current. The variables l and A represent the length and cross-sectional area of the conductor, respectively. These variables are directly proportional to the current, meaning that as the length or cross-sectional area increases, the current also increases.

3. What units are used for each variable in the Rnet~l2/A formula?

The current (I) is measured in amperes (A), the resistance (Rnet) is measured in ohms (Ω), the length (l) is measured in meters (m), and the cross-sectional area (A) is measured in square meters (m2).

4. Can the Rnet~l2/A formula be used for both direct and alternating current?

Yes, the Rnet~l2/A formula can be used for both direct and alternating current. However, for alternating current, the formula is usually written as I = V/Rnet, where V represents the voltage in volts (V). This is because for alternating current, the resistance can vary with the frequency of the current.

5. How is the Rnet~l2/A formula used in real-world applications?

The Rnet~l2/A formula is used in a variety of real-world applications, such as designing electrical circuits, calculating the power consumption of household appliances, and determining the appropriate wire gauge for a given length and current. It is also used in industries such as electronics, telecommunications, and power generation and distribution to ensure the safe and efficient flow of electricity.

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