Question

The voltage and current at the input of the following network are given by the expressions (V(t) = 2 sin(3t)) and (I(t) = 3 cos(3t)). Calculate the average power absorbed by the network.

a) (P_avg = 6 , W)
b) (P_avg = 0 , W)
c) (P_avg = 9 , W)
d) (P_avg = 18 , W)

Answer 1

The average power absorbed by the network is zero watts (P_avg = 0 W), because the current leads the voltage by 90 degrees, resulting in a cosine of the phase difference that is equal to zero.

Step-by-step explanation:

To calculate the average power absorbed by the network, we can use the formula for average power in an AC circuit, Pavg = Irms Vrms cos(φ), where φ is the phase difference between the voltage and the current. Since we are given V(t) = 2 sin(3t) and I(t) = 3 cos(3t), we can see that the current leads the voltage by 90 degrees (φ = 90°), resulting in a cos(φ) of 0. This means that the average power absorbed by the network is zero, as cos(90°) = 0, thus option b) Pavg = 0 W is the correct answer.