# Electric current function of time

1. Dec 28, 2014

### Karol

1. The problem statement, all variables and given/known data
$i=20\sin(377t)$ is the current function. in the time interval 0-1/120 sec what is the charge that passed

2. Relevant equations
$$q=\int_0^t i dt$$

3. The attempt at a solution
$$q=\int_0^{1/120} 20\sin(377t) dt=\frac{20}{377}\int_0^{3.14} \sin x dx$$
$$q=-\frac{20}{377}\cos x|_0^{3.14}=-\frac{20}{377}(-0.0015)=79.6\cdot10^{-6}[Coulomb]$$
It should be q=0.106

2. Dec 28, 2014

### Bystander

Okay.
Huh?

3. Dec 28, 2014

### Karol

One word is enough, thanks

4. Dec 28, 2014

### haruspex

Maybe, but I'll add few anyway.
It's not a good idea to substitute numbers in prior to the final step, particularly if they're only approximations.
$\cos(\pi)$ is exactly -1, and you should not be using a calculator for that.