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

[Kawrae]

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?

 

[Doc Al]

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.

 

[Kawrae]

? 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?

 

[Doc Al]

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!