Answer:
Power factor is 0.8517 or 85.17%
Step-by-step explanation:
We are given that in a parallel circuit, [tex]E_{T}=208V[/tex], R=39kΩ and [tex]X_{L}[/tex]=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,
[tex]I_{R} =\frac{E_{T}} {R}= \frac{208}{39} =\frac{16}{3}=5.33[/tex] milli amps
And current through inductor,[tex]I_{L} =\frac{E_{T}} {X_{L}} =\frac{208}{24}=\frac{26}{3}=8.667[/tex] milli amps.
Hence total current, [tex]I_{T}= \sqrt{(I_{R})^2+(I_{T})^{2}} =\sqrt{5.33^{2}+8.667^{2}}=10.176[/tex]
Now power factor=[tex]\frac{I_{R}}{I_{T}}=\frac{5.33}{10.176}=0.8517[/tex]
Hence power factor is 85.17% or 0.8517
