Electric Current as a function of time

[jmuduke]

Homework Statement

8. An electric current in a conductor varies with time according to the expression
I(t) = 100 sin (120*pi*t), where I is in amperes and t is in seconds. What is the total charge passing a given point in the conductor from t = 0 to t = 1/240 s?

Homework Equations

The Attempt at a Solution

I have attempted to substitute the values of t into the equation and use the difference, but I do not feel that was the correct way. Next, I attempted to perform a definite integral, but I get 0 for both numbers.

 

[tiny-tim]

welcome to pf!

hi jmuduke! welcome to pf!

I(t) = 100 sin (120*pi*t), where I is in amperes and t is in seconds. What is the total charge passing a given point in the conductor from t = 0 to t = 1/240 s?
…
I attempted to perform a definite integral, but I get 0 for both numbers.

yes, I = dQ/dt, so Q = ∫ I dt

it's only over 90°, so you shouldn't get 0 for both limits

show us what you did ​

 

[jmuduke]

Thanks for the reply Tim!

I calculated the integral and got -(5 cos(120*pi*t))/6*pi

Originally, my calculator was set in radians, so that could have been why I got 0 for both limits. I changed it to degrees and got -0.265 for both limits then, but that result in the definite integral being 0, correct?

 

[tiny-tim]

hi jmuduke!

(just got up :zzz:)

I calculated the integral and got -(5 cos(120*pi*t))/6*pi

… got -0.265 for both limits then, but that result in the definite integral being 0, correct?

yes, cos(0) = 1, so that's correct for the t = 0 limit

but for t = 1/240, cos(120πt) = cos(π/2) = cos90° = 0 ​