If the current and voltage of an electrical device (in the passive reference configuration) are v \left (t \ right) v (t) = 6 \sin\left(100\pi t\right)sin(100πt) V and i\left(t\right)i(t) = 6 \sin\left (100 \ pi t \ right) sin (100πt) + 9 \cos \left (100\pi t\right) cos (100πt) A. Then the average power delivered to the device (computed to one decimal place) is given by:.

The average power is 18 W

Explanation:

Solution:-

If the current and voltage of an electrical device (in the passive reference configuration) are:

                         v(t) = 6 sin(100πt) V  

                         i(t) = 6 sin(100πt) + 9 cos(100πt) Amp

- First we will find the harmonic form of the current function i(t):

                 a sin ( wt ) + b cos ( wt ) ≡ R*sin ( wt + α )

Where,

                 R = √( a^2 + b^2 )

                 α = arctan ( b / a )  

- Transforming the function i (t) into the harmonic form:

                a = 6 , b = 9

                 R = √( a^2 + b^2 ) = √( 6^2 + 9^2 ) = √( 36 + 81 )

                R = √117

                 α = arctan ( b / a ) = arctan ( 9 / 6 )

                 α = 0.98279 rads

Hence,

                  i(t) = 6 sin(100πt) + 9 cos(100πt) ≡ √117*sin (100πt + 0.98279 )

- The average power is given by the following formula:

Where,

                 Vm: The mean voltage

                 Im : The mean current

                 β : The phase difference

- Using the given functions we have:

                Vm = 6 V , Im = R = √117 Amps , β = 0.98279

The average power is 18 W.

18W

Explanation:

To find the average power of the electrical device you use the following formula:

T: period of the oscillation

i(t): current

v(t): voltage

By replacing i and v in the integral and solve it you obtain:

The solution of the integral is attached below:

By replacing the value of the integral (9/25) you obtain:

hence, the power of the device is 18W

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

i think it would be 5