Electric current function of time

[Karol]

Homework Statement

$i=20\sin(377t)$ is the current function. in the time interval 0-1/120 sec what is the charge that passed

Homework Equations

$$q=\int_0^t i dt$$

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

 

[Bystander]

cosx| 3.14 0

Okay.

(−0.0015)=

Huh?

 

[Karol]

One word is enough, thanks

 

[haruspex]

One word is enough, thanks

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.

 

[asteriatic]

C

Based on the given current function and the time interval, the charge that has passed can be calculated using the equation q = ∫_0^t i dt. The integral of the current function from 0 to 1/120 seconds is equal to the charge that has passed in that time interval. Using the given values, the equation becomes q = ∫_0^1/120 20sin(377t) dt. Solving this integral, we get q = -20/377cos(377t)|_0^1/120. Plugging in the limits of integration, we get q = -20/377(cos(377/120)-cos(0)). Simplifying, we get q = -20/377(cos(3.14)-1). This gives us q = 20/377(1-cos(3.14)) = 20/377(1+0.0015) = 20/377(1.0015) = 0.053 C. Therefore, the charge that has passed in the time interval 0-1/120 seconds is 0.053 C.