How Do You Calculate the Total Charge from a Sine Wave Current?

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To calculate the total charge from a sine wave current given by I(t) = 115 sin(120t), one must integrate the current over the specified time interval from t = 0 to t = 1/120 seconds. The relationship I = dQ/dt indicates that the charge Q can be found by integrating the current function. The correct approach involves setting up the integral of I(t) with respect to time, not merely evaluating the current at specific time points. This integration will yield the total charge carried by the current during the given time frame. Understanding that the integral of the current provides the total charge is crucial for solving this problem.
Kawrae
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An electric current is given by the expression I ( t ) = 115 sin(120t), where I is in amperes and t is in seconds. What is the total charge carried by the current from t = 0 to t = 1/120 s?

>> Since I = deltaQ/deltaT I rearranged and solved for Q = I(deltaT).

Then I took T=0 and plugged it into the I formula they gave. Then I plugged T=1/120 into that formula. And subtracted the two answers to get 0.008362. Then I tried taking this answer and multipling it by (1/120) to get Q. I don't think I did this right, but I don't really know how to go about finding the right answer :(

Any ideas?
 
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Kawrae said:
An electric current is given by the expression I ( t ) = 115 sin(120t), where I is in amperes and t is in seconds. What is the total charge carried by the current from t = 0 to t = 1/120 s?
I presume (120t) is in radians?

>> Since I = deltaQ/deltaT I rearranged and solved for Q = I(deltaT).
I presume you integrated?

Then I took T=0 and plugged it into the I formula they gave.
What formula? All you needed to do was integrate over given range.
 
? I'm confused on what I'm supposed to integrate -> the original I(t) that they gave me? Won't that just give me the current when they want the charge?
 
Since the current is the time derivative of charge (I = dQ/dt), the charge is the integral (anti-derivative) of the current:
dQ/dt = 115 sin(120t)
dQ = 115 sin(120t) dt
Integrate!
 
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