Current density in a wire that is being used to charge a capacitor

In summary: So you would be wise to report your answer as 3 m/s and not 3.0 m/s.In summary, the conversation discusses the correct calculation of instantaneous rate of change in a wire. It is explained that the equation I=Q/t cannot be used in this situation and instead, derivatives must be used. It is also noted that the specified units of 0.7mm² and 2s should only be reported to 1 significant figure.
  • #1
Ugnius
54
10
Homework Statement
Wire, with diameter of 0.7 mm2, is used to charge a capacitor. Charge on the capacitor plate is described as: Q(t):=4*t^3+5*t+3 [C]. What is current density in a wire, at given time t=2s?
Relevant Equations
Q(t):=4*t^3+5*t+3 , j=I/A , I=Q/t
1634575431520.png

Somehow this answer is incorrect , but i realize that even numbers are hipothetical , 45 coulumbs is too much charge , what is wrong in my calculations?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Q(t) is the total charge on the capacitor, including what has accumulated in the past. The current in the wire is the rate at which new charge is added/removed.
 
  • Like
Likes Ugnius
  • #3
Okay , but I = Q/t so that's 12.5 A in the wire at the moment t=2, but why isn't the answer correct , is there some kind of a mistake in calculation?
 
  • #4
As @DaveE pointed out, the current I in the wire at the instant t = 2 s is the instantaneous rate at which charge is flowing through a cross-section of the wire. This must equal the instantaneous rate at which charge is arriving at the plate of the capacitor at t = 2.

How do you calculate the instantaneous rate of change of some function of time?
 
Last edited:
  • Like
Likes Ugnius
  • #5
Ugnius said:
Homework Statement:: Wire, with diameter of 0.7 mm2,
A diameter could have units of mm, but not mm2.
 
  • Like
Likes Ugnius
  • #6
Ugnius said:
what is wrong in my calculations?
The equation I=Q/t can’t be used here. This equation applies to situations where current is constant or we only want the average current. T help you understand your mistake, try this problem:

An object moves along a straight line so its distance (x) from a reference point (x=o) is given by:
x(t) = 4t³ + 5t + 3
Q1. What is the object’s average speed during the interval t=0 to t=2s?
Q2. What is the object’s speed at the instant t=2s?
_____________

Also note “Wire, with diameter of 0.7 mm2” doesn’t make sense. You probably mean:
“Wire, with cross-sectional area of of 0.7 mm²” or
“Wire, with diameter of 0.7 mm”
You need to be certain which one it is.

@Edit. @TSny beat me to it!
 
  • Like
Likes Ugnius
  • #7
Thanks guys , I managed to solve it using derivatives , your help much appreciated.
1634582860819.png
 
  • Like
Likes Steve4Physics, DaveE and TSny
  • #8
Congratulations, good work!
 
  • #9
Ugnius said:
Thanks guys , I managed to solve it using derivatives , your help much appreciated.
View attachment 290868
Well done. But don't forget that 0.7mm² and 2s are each specified to only 1 significant figure.
 

FAQ: Current density in a wire that is being used to charge a capacitor

What is current density and how is it related to charging a capacitor?

Current density is a measure of the amount of electric current flowing through a unit area of a material. In the context of charging a capacitor, current density refers to the flow of electrons through a wire that is connected to the capacitor. As the capacitor charges, the current density in the wire increases.

How does the current density in the wire affect the charging time of the capacitor?

The current density in the wire directly affects the charging time of the capacitor. A higher current density means that more electrons are flowing through the wire, which leads to a faster charging time for the capacitor. Conversely, a lower current density will result in a slower charging time for the capacitor.

What factors can affect the current density in the wire during capacitor charging?

The current density in the wire can be affected by several factors, including the resistance of the wire, the voltage applied to the capacitor, and the capacitance of the capacitor. A higher resistance or lower voltage will result in a lower current density, while a higher capacitance will lead to a higher current density.

How does the current density in the wire change as the capacitor reaches full charge?

As the capacitor reaches full charge, the current density in the wire decreases. This is because the capacitor has reached its maximum capacity to store electrons, so the flow of current through the wire decreases. At this point, the current density will remain constant until the capacitor is discharged or the voltage is changed.

Can the current density in the wire become too high during capacitor charging?

Yes, the current density in the wire can become too high during capacitor charging. This can lead to overheating and potentially damage to the wire or other components. It is important to use the appropriate wire size and to monitor the current density to prevent any potential issues.

Similar threads

Finding Current in Resistors & Charge of Capacitor
Replies
4
Views
1K
Final Charge of a Capacitor in a Circuit with Capacitors and Resistors
Replies
9
Views
1K
Induction heat flux density induced by wire in a slab
Replies
0
Views
451
Capacitor Questions Charging and Discharging
Replies
4
Views
2K
I Thought I Understood Gauss' Law (Sheets)
Replies
26
Views
1K
Relationship between radial distance and charge density of a capacitor
Replies
2
Views
2K
A uniformly charged rotating sphere does not radiate, why not?
Replies
4
Views
1K
Electric Field Inside Cylindrical Capacitor
Replies
2
Views
2K
Surface Current and Electric Field
Replies
1
Views
1K
Help with Mathematical Description & Calculations of Space Charge Density
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top