Question

A sinusoidal voltage source with instantaneous voltage v(t)= 120√2sin (120πt 30∘), is applied to a series RL load and the resulting current in Fourier series form is i(t)= 4 + 6√2 sin (120πt) + 22 sin (240πt) . Determine

a. The average power absorbed by the load.

Answer 1

a. The average power absorbed by the load is given by the formula P_avg = I_dc^2 * R, where I_dc is the DC component of the current and R is the resistance.

Step-by-step explanation:

The average power absorbed by the load can be calculated using the formula P = Iavg * Vavg * cos(θ), where Iavg is the average current, Vavg is the average voltage, and θ is the phase angle between the voltage and current.

Given the Fourier series form of the current i(t) = 4 + 6√2 sin(120πt) + 22 sin(240πt), we can see that the average component of the current is 4. Therefore, Iavg = 4.

The average voltage can be obtained from the equation v(t) = 120√2sin(120πt + 30°). Taking the average value of the sinusoidal function, we get Vavg = 120√2 / √2 = 120 V.

As the phase angle is not specified in the question, we cannot calculate the power.