Mathematics: I need help with these 2

I need help with these 2 - id211988223, organicmemez

shadowsnake

28.03.2021

Power factor is 0.8517 or 85.17%

Step-by-step explanation:

We are given that in a parallel circuit, $E_{T}=208V$ , R=39kΩ and $X_{L}$ =24kΩ.

That means the circuit has a resistor element, inductor element in parallel with 208V applied across the terminal.

Let us find the current through resistor,

$I_{R} =\frac{E_{T}} {R}= \frac{208}{39} =\frac{16}{3}=5.33$ milli amps

And current through inductor, $I_{L} =\frac{E_{T}} {X_{L}} =\frac{208}{24}=\frac{26}{3}=8.667$ milli amps.

Hence total current, $I_{T}= \sqrt{(I_{R})^2+(I_{T})^{2}} =\sqrt{5.33^{2}+8.667^{2}}=10.176$

Now power factor= $\frac{I_{R}}{I_{T}}=\frac{5.33}{10.176}=0.8517$

Hence power factor is 85.17% or 0.8517

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