Question

The current in a ˚uit is (45 + j12 , {A}) when the voltage is (82 + j100 , {V}). Determine the phase angle between voltage and current, the power factor, the active power, the reactive power, and the apparent power in the ˚uit.

Answer 1

The phase angle between voltage and current is determined using the arctangent function on the quotient of their imaginary and real parts. The power factor is the cosine of this angle, with active, reactive, and apparent power calculated using their respective formulas involving rms values and trigonometric functions of the phase angle.

Step-by-step explanation:

To determine the phase angle between voltage and current, we can use the phasors given for current and voltage. The current in the circuit is given as (45 + j12) A, and the voltage is given as (82 + j100) V. We can calculate the phase angle θ using the arctangent of the imaginary part over the real part of the voltage divided by the current. The phase angle is θ = arctan((100/82)/(12/45)).

The power factor (PF) is the cosine of the phase angle, which signifies the ratio of the active power to the apparent power. The formula for power factor is PF = cos(θ). The active power (P), also known as the real power, can be calculated using P = Vrms * Irms * cos(θ), where Vrms and Irms are the root mean square values of voltage and current, respectively. The reactive power (Q) can be determined using Q = Vrms * Irms * sin(θ), and the apparent power (S) is given by S = Vrms * Irms.