Electric current function of time

Click For Summary

Homework Help Overview

The discussion revolves around determining the charge that passes through a circuit given the current function \(i=20\sin(377t)\) over a specified time interval. The problem is situated within the context of electric circuits and involves integration to find the charge from the current function.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the integration of the current function to find the charge, with one participant attempting to compute the integral directly. Questions arise regarding the accuracy of numerical substitutions and the use of approximations in calculations.

Discussion Status

The discussion is ongoing, with participants providing feedback on the calculations presented. There is a focus on the importance of exact values versus approximations in mathematical expressions, indicating a productive exploration of the problem.

Contextual Notes

Participants are considering the implications of using approximations in calculations and the potential impact on the final result. The original poster's calculations and assumptions are being scrutinized for accuracy.

Karol
Messages
1,380
Reaction score
22

Homework Statement


##i=20\sin(377t)## is the current function. in the time interval 0-1/120 sec what is the charge that passed

Homework Equations


$$q=\int_0^t i dt$$

The Attempt at a Solution


$$q=\int_0^{1/120} 20\sin(377t) dt=\frac{20}{377}\int_0^{3.14} \sin x dx$$
$$q=-\frac{20}{377}\cos x|_0^{3.14}=-\frac{20}{377}(-0.0015)=79.6\cdot10^{-6}[Coulomb]$$
It should be q=0.106
 
Physics news on Phys.org
Karol said:
cosx| 3.14 0
Okay.
Karol said:
(−0.0015)=
Huh?
 
One word is enough, thanks
 
Karol said:
One word is enough, thanks
Maybe, but I'll add few anyway.
It's not a good idea to substitute numbers in prior to the final step, particularly if they're only approximations.
##\cos(\pi)## is exactly -1, and you should not be using a calculator for that.
 

Similar threads

Replies
3
Views
2K
Replies
11
Views
2K
Replies
7
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
12
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
1
Views
3K