/sci/ - Science & Math

>>11785881
My first love ;_;

>>11653377
>>11653493
>>11653667
You need to be patient, hunny~! I'm assuming the 240 volts is rms. Let w=2pi*50, P=30 kW and Q=20 kVAr so that S=P+jQ.
>i
[math] PF=\cos\theta=1\implies \theta=0,\ Q'=0 [/math]. So [math] S=P=30\text{ kW} [/math] and the reactive power due to the capacitor is [math] Q_C=Q-Q'=20\text{ kVAr} [/math]. Finally, [math] C=Q_c/\omega V_{rms}^2=20000/(2\pi\cdot50\cdot240^2)=1.11\text{ mF} [/math]
>ii
[math]PF=\cos\theta=.95\implies\theta=18.19^\circ ,\ Q'=P\tan\theta=9.86\text{ kVAr}[/math]. Now [math] Q_C=Q-Q'=10.14\text{ kVAr} [/math] and [math] C=Q_C/\omega V_{rms}^2=10139/(2\pi\cdot50\cdot240^2)=560\ \mu\text{F} [/math]
Obviously you need to check my work.
>>11653754
You're taking a magnitude. The magnitude of a the ratio of two complex numbers is the ratio of the magnitudes.
>>11653856
probably ecological if not social catastrophe. i like trees. this sound like a dark future. im not really sure what kinda response you were after.