Charge passing through a cross section for a time varying current

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SUMMARY

The discussion centers on calculating the total charge passing through a cross-section of a wire with a time-varying current described by the equation I(t) = 6.00 A + (4.80 A/s)t. The correct method involves integrating the current over the time interval from t = 0.00 s to t = 3.00 s, leading to the result of q = 39.6 coulombs. The initial miscalculation of q = 75.6 coulombs was due to an error in the integration process. The final answer confirms the importance of accurately applying calculus to solve problems involving variable currents.

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  • Understanding of calculus, specifically integration techniques.
  • Familiarity with electrical current concepts, particularly the relationship between current and charge.
  • Knowledge of the fundamental equation I = dq/dt.
  • Experience with solving differential equations related to electrical circuits.
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  • Review integration techniques for variable functions in calculus.
  • Study the relationship between current and charge in electrical circuits.
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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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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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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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