Calculating Current in a Wire: Applying PD and Cross-Sectional Area

In summary, the conversation discusses a scenario where a pd is applied across different faces of a rectangle and how it affects the current and resistance. The correct answer is D because both the distance the current has to travel and the area the current moves through change, resulting in a quarter of the original resistance. The relevant equation is R \propto \frac{l}{A} where l is the length of the resistor and A is the cross-sectional area.
  • #1
ravsterphysics
57
1

Homework Statement


1.JPG


Homework Equations

The Attempt at a Solution



I know I = nqvA

When the pd is applied the surface that is 8cm long, the cross sectional area is 32cm (8x4) but when the pd is applied across the 4cm side, the cross sectional area is now 16cm (4x4) so I has decreased by a factor of 2 so the new I is I/2 thus answer A? But the correct answer is D.
 
Physics news on Phys.org
  • #2
When comparing I=nqvA for each case, you assumed that only A changed. q stays the saem OK - but is v the same?
HInt: Ohms' law and resistivity.
 
  • Like
Likes ravsterphysics
  • #3
You've got the order of the faces backwards. The initial scenario has the PD applied across the ends of the rectangle (the 4 x 4 ends are separated by 8 cm).

Also, remember that resistance is proportional to path length as well as being inversely proportional to the cross sectional area. Look up the definition of resistivity.
 
  • Like
Likes ravsterphysics
  • #4
ravsterphysics said:

Homework Statement


View attachment 111643

Homework Equations

The Attempt at a Solution



I know I = nqvA

When the pd is applied the surface that is 8cm long, the cross sectional area is 32cm (8x4) but when the pd is applied across the 4cm side, the cross sectional area is now 16cm (4x4) so I has decreased by a factor of 2 so the new I is I/2 thus answer A? But the correct answer is D.

I think that the relevant equation is: [itex]R \propto \frac{l}{A}[/itex] where [itex]l[/itex] is the length of the resistor and [itex]A[/itex] is the cross-sectional area. Switching from one face to the other changes both [itex]A[/itex] and [itex]l[/itex].
 
  • Like
Likes ravsterphysics
  • #5
People are always very quick to use formulas ... much easier just to look at it ...the distance the current has to travel has halved so this alone will make the resistance halve ... but in addition the area the current moves through has doubled .. this will also halve the resistance ... so in total the resistance has dropped to a quarter of what it was ...
 
  • Like
Likes ravsterphysics
  • #6
Simon Bridge said:
When comparing I=nqvA for each case, you assumed that only A changed. q stays the saem OK - but is v the same?
HInt: Ohms' law and resistivity.

gneill said:
You've got the order of the faces backwards. The initial scenario has the PD applied across the ends of the rectangle (the 4 x 4 ends are separated by 8 cm).

Also, remember that resistance is proportional to path length as well as being inversely proportional to the cross sectional area. Look up the definition of resistivity.

stevendaryl said:
I think that the relevant equation is: [itex]R \propto \frac{l}{A}[/itex] where [itex]l[/itex] is the length of the resistor and [itex]A[/itex] is the cross-sectional area. Switching from one face to the other changes both [itex]A[/itex] and [itex]l[/itex].

oz93666 said:
People are always very quick to use formulas ... much easier just to look at it ...the distance the current has to travel has halved so this alone will make the resistance halve ... but in addition the area the current moves through has doubled .. this will also halve the resistance ... so in total the resistance has dropped to a quarter of what it was ...

Yep, I totally disregarded the effects on the wire's resistance. It's clear now why current goes up by a factor of 4. thanks for the help.
 
  • Like
Likes Simon Bridge

1. What is current in a wire?

Current in a wire refers to the flow of electric charge, typically in the form of electrons, through a conducting material such as a wire. It is measured in amperes (A) and is a fundamental concept in electricity and magnetism.

2. How is current in a wire measured?

Current in a wire is measured using a device called an ammeter. The ammeter is connected in series with the wire, allowing it to measure the amount of current passing through the wire at a specific point. The unit of measurement for current, amperes, is named after the French physicist Andre-Marie Ampere.

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

The amount of current in a wire is affected by several factors, including the voltage applied to the wire, the resistance of the wire, and the length and thickness of the wire. Ohm's Law states that current is directly proportional to voltage and inversely proportional to resistance.

4. How does current in a wire create a magnetic field?

When current flows through a wire, it creates a circular magnetic field around the wire. The strength of the magnetic field is directly proportional to the amount of current flowing through the wire. This phenomenon is the basis for electromagnets, which are used in a variety of applications, including motors and generators.

5. What are some real-world applications of current in a wire?

Current in a wire has numerous real-world applications, including powering electronic devices, lighting buildings and homes, and transmitting electricity over long distances. It is also essential in various technologies, such as electric motors, generators, and transformers. Additionally, current in a wire is used in medical equipment, such as MRI machines, and in scientific instruments, such as spectrometers.

Similar threads

  • Introductory Physics Homework Help
Replies
22
Views
6K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
797
  • Introductory Physics Homework Help
Replies
19
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top