The voltage across the load is given by v(t) = 50sin(314t-45) and the current through the load is given by I(t) = 100sin(314t-60).


Active power is the average power consumed by the load and is given by the formula P = Vrms * Irms * cos(θ), where Vrms is the root mean square voltage, Irms is the root mean square current, and θ is the phase difference between voltage and current.

To calculate Vrms, we first need to find the amplitude of the voltage waveform. Since the voltage waveform is given by v(t) = 50sin(314t-45), the amplitude is 50.

Vrms = (Amplitude / sqrt(2)) = (50 / sqrt(2))

To calculate Irms, we need to find the amplitude of the current waveform. Since the current waveform is given by I(t) = 100sin(314t-60), the amplitude is 100.

Irms = (Amplitude / sqrt(2)) = (100 / sqrt(2))

The phase difference between voltage and current is given by the difference in their phase angles, which is 60 - (-45) = 105 degrees.

Now we can calculate the active power:

P = Vrms * Irms * cos(θ) = (50 / sqrt(2)) * (100 / sqrt(2)) * cos(105 degrees)


Reactive power is the power consumed by the load that is out of phase with the voltage and is given by the formula Q = Vrms * Irms * sin(θ), where Vrms is the root mean square voltage, Irms is the root mean square current, and θ is the phase difference between voltage and current.

Using the values of Vrms, Irms, and θ calculated earlier, we can calculate the reactive power:

Q = Vrms * Irms * sin(θ) = (50 / sqrt(2)) * (100 / sqrt(2)) * sin(105 degrees)


The active power consumed by the load is calculated to be P = (50 / sqrt(2)) * (100 / sqrt(2)) * cos(105 degrees).
The reactive power consumed by the load is calculated to be Q = (50 / sqrt(2)) * (100 / sqrt(2)) * sin(105 degrees).

Note: The values of Vrms and Irms are divided by sqrt(2) to convert the amplitudes to root mean square values. This is necessary because the power formulas involve the square of the voltage and current values.