Charge passing through a cross section for a time varying current

In summary, the current in a wire is given by the equation I(t) = 6.00 A + (4.80 A/s)t and we need to find the amount of charge that passes through a cross section of the wire in the time period between t = 0.00 s and 3.00 s. To do this, we use the equation q = ∫I(t)dt and integrate from 0 to 3 seconds, resulting in q = 39.6 coulombs. The mistake was likely due to an incorrect input of the equation.
  • #1
superslow991
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1

Homework Statement


The current in a wire varies with time according to the equation I(t) = 6.00 A + (4.80 A/s)t, where t is in seconds. How many coulombs of charge pass a cross section of the wire in the time period between t = 0.00 s and 3.00 s

Homework Equations


I=dq/dt

The Attempt at a Solution


So since were calculating the current, i solved for q=(integral)I*dt which was the integral from 0 to 3 (6.00A+(4.80)t and got the answer q = 75.6 which is wrong. The answer is q= 39.6.
I know the problem lies in the math but I am not sure where I am wrong.
 
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  • #2
Can you write out your steps in performing your integral so we can see where you made a mistake.

Edit: Maybe you attempted to post a picture and it didn't show up.
 
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  • #3
TomHart said:
Can you write out your steps in performing your integral so we can see where you made a mistake.

Edit: Maybe you attempted to post a picture and it didn't show up.
Actually i think i input my equation wrong i got the right answer
 
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1. How is charge passing through a cross section measured for a time-varying current?

The charge passing through a cross section for a time-varying current is measured using an ammeter, which measures the amount of charge passing through a specific point in a circuit over a given time interval.

2. What factors affect the amount of charge passing through a cross section for a time-varying current?

The amount of charge passing through a cross section for a time-varying current is affected by the magnitude and direction of the current, the cross-sectional area of the conductor, and the duration of the current flow.

3. How does the charge passing through a cross section change when the current is time-varying?

When the current is time-varying, the charge passing through a cross section also varies over time. This is because the amount of charge flowing through a conductor is directly proportional to the current, and as the current changes, so does the charge passing through the cross section.

4. What is the relationship between charge passing through a cross section and the current's frequency?

The frequency of the current has a direct impact on the amount of charge passing through a cross section. As the frequency increases, the current alternates more rapidly, resulting in a higher charge passing through the cross section over a given time interval.

5. How does the charge passing through a cross section for a time-varying current affect the strength of an electromagnetic field?

The amount of charge passing through a cross section for a time-varying current directly affects the strength of the electromagnetic field produced by the current. As more charge passes through the cross section, the strength of the field increases, and vice versa.

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