Question

Find the complex power for the following:

Vrms​=180∠30∘ V,Z=40 + j60Ω
The complex power is ___

Answer 1

To find the complex power, convert Vrms to phasor form, calculate the complex conjugate of the impedance, derive the rms current's complex conjugate, and multiply the phasor voltage by this conjugate current.

Step-by-step explanation:

To find the complex power for the given electrical circuit with Vrms​=180∠30° V and Z=40 + j60Ω, we will follow these steps:

1. First, we must convert the root mean square (Vrms) voltage to its phasor form, which is already given as 180∠30°.
2. Next, we compute the complex conjugate of the impedance Z, which is Z* = 40 - j60Ω.
3. Finally, the complex power S is given by S = Vrms x I*rms, where I*rms is the complex conjugate of the rms current Irms. We obtain Irms by dividing Vrms by Z. Therefore, Irms = Vrms / Z.
4. Using the given values, we calculate Irms = 180∠30° / (40 + j60) Ω.
5. To find I*rms, we take the complex conjugate of Irms = 180∠30° / (40 + j60).
6. Finally, we find S by multiplying the phasor form of Vrms by I*rms.

Note that in the final calculation, the angle of Vrms adds to the negative of the angle of Irms, because we are using the complex conjugate of the current.