Calculating Charge Entering an Element: Q=6.667 C

[Wolverine31]

Homework Statement

The current flowing through an element is i = 2 A for 0<t<1 and i = 2t^2 A for t>1
Calculate the charge entering the element from t=0s to t=2s.
Answer: 6.667 C.

Homework Equations

I used Q=t1∫t2 i dt

The Attempt at a Solution

I tried to solve using integral method. but how to proceed here as for 0<t<1 i is constant and i am stuck. Are there any other methods.

 

[Wolverine31]

I think this is a very basic problem but still I cannot do it because i am a newbie and may be to need work harder. Sorry for consuming your time.

 

[SteamKing]

If the current is constant over a given time interval, how much charge is accumulated? Remember, 1 ampere = 1 coulomb / second.

Why did you chose the integral method to solve this problem if you cannot integrate a constant function?

 

[Wolverine31]

If the current is constant over a given time interval, how much charge is accumulated? Remember, 1 ampere = 1 coulomb / second.

Why did you chose the integral method to solve this problem if you cannot integrate a constant function?

Thank you for pointing out. I made this post in hurry without thinking. And now i got the answer myself.

for 0s to 1s i = 2A so q = 2C

for 1s to 2 s i calculated by integrating i wrt dt between 1s to 2s

and added two values and the answer is correct.

 

[Nickie]

Yes, there are other methods that can be used to solve this problem. One method is to break the time interval into two parts (0<t<1 and t>1) and calculate the charge for each interval separately. For 0<t<1, the charge entering the element would be Q = i*t = 2*1 = 2 C. For t>1, the charge would be Q = t1∫t2 i dt = 2∫1 2t^2 dt = 2[t^3/3]1 = 2*(1/3) = 0.667 C. Therefore, the total charge entering the element from t=0s to t=2s would be 2+0.667 = 2.667 C. This is slightly different from the given value of 6.667 C, so it is important to double check the given values and equations used for calculation.