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QJEEM21Phaacb: JEE Main 2021 Physics - Class 12 JEEM21Phaacb Solution: An ac circuit has an inductor and a resistor resistance R in…

An ac circuit has an inductor and a resistor resistance R in series, such that XL = 3R. Now, a capacitor is added in series such that XC = 2R. The ratio of new power factor with the old power factor of the circuit is 5:x\sqrt 5 :x . The value of x is ___________.

Step-by-Step Verified Solution

JEE Main 2021 (Online) 27th August Evening Shift Physics - Alternating Current Question 91 English Explanation
cos⁡ϕ=RR2+3R2\cos \phi = {R \over {\sqrt {{R^2} + 3{R^2}} }}

=110= {1 \over {\sqrt {10} }}

cos⁡ϕ′=RR2+R2\cos \phi ' = {R \over {\sqrt {{R^2} + {R^2}} }}

=12= {1 \over {\sqrt 2 }}

cos⁡ϕ′cos⁡ϕ=102=51{{\cos \phi '} \over {\cos \phi }} = {{\sqrt {10} } \over {\sqrt 2 }} = {{\sqrt 5 } \over 1}

∴\therefore x = 1

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