Question

Assume the voltage across a load is given by v(t)=60cos(ωt−10∘)V and the current through the load (in the direction of the voltage drop) is i(t)=1.5cos(ωt+50∘). Find: Complex power S and apparent power S

Answer 1

The complex power S and apparent power S for a load with the given voltage v(t)=60cos(ωt−10°)V and current i(t)=1.5cos(ωt+50°)A are 90∠40° VA and 90 VA, respectively.

Step-by-step explanation:

The student has asked for the calculation of complex power S and apparent power S when the voltage across a load is given by v(t)=60cos(ωt−10°)V and the current through the load is i(t)=1.5cos(ωt+50°)A. We'll need to employ phasor representation to compute these values. Complex power S in a circuit is represented as S = V * I*, where V is the phasor of the voltage and I* is the conjugate of the current phasor.

First, we convert the given voltage and current to phasor form:

• Voltage phasor V = 60∠−10° V
• Current phasor I = 1.5∠50° A

The complex power S is then:

S = (60∠−10°)(1.5∠−50°)*

= (60)(1.5)∠(−10° - (-50°))

= 90∠40° VA

The apparent power S is the magnitude of complex power, which is:

S = |90∠40°|

= 90 VA

Therefore, the complex power is 90∠40° VA, and the apparent power is 90 VA.