A series LCR circuit with a 100 ohm resistor dissipates 80 W when attached to a 120 V, 60 Hz power line. What is the power factor?

Asked by arjunsah797 | 27th Mar, 2022, 08:00: PM

Expert Answer:

Power dissipation in 100 Ω resistor = begin mathsize 14px style i subscript r m s end subscript superscript 2 R end style = 80 W
where irms is RMS current in the circuit and R is resistor
 
begin mathsize 14px style i subscript r m s end subscript space equals space square root of 80 over 100 end root space equals space 0.894 space A end style
Impedence z of circuit is calculated as follows
 
begin mathsize 14px style z space equals space v subscript r m s end subscript over i subscript r m s end subscript space equals space fraction numerator 120 over denominator 0.894 end fraction space equals space 134 space capital omega end style

Impedence z of circuit is given as
 
begin mathsize 14px style z space equals space square root of R squared plus left parenthesis X subscript C minus X subscript L right parenthesis squared end root space equals space 134 space capital omega end style
begin mathsize 14px style R squared space plus space open parentheses X subscript C minus X subscript L close parentheses squared space equals space 18000 end style
begin mathsize 14px style open parentheses X subscript C minus X subscript L close parentheses space equals space square root of 18000 minus 10000 end root space equals space 89.4 space capital omega end style
 
Power factor = cosΦ ,
 
where Φ = tan-1 [ ( XC - XL ) / R ] = tan-1 [ 89.4 / 100 ] = 41.81 o
 
power factor = cosΦ = cos ( 41.81 ) = 0.745

Answered by Thiyagarajan K | 27th Mar, 2022, 09:08: PM