Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

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 | 27 Mar, 2022, 08:00: PM
answered-by-expert 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 | 27 Mar, 2022, 09:08: PM
CBSE 12-science - Physics
Asked by arjunsah797 | 27 Mar, 2022, 08:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by saivardhanreddy15022003 | 11 Mar, 2022, 06:47: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by rishicool0205 | 19 Aug, 2020, 02:20: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by rajneetverma11 | 16 Feb, 2020, 04:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by Topperlearning User | 22 Jun, 2015, 10:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by Topperlearning User | 22 Jun, 2015, 10:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Asked by Topperlearning User | 22 Jun, 2015, 10:58: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×