JEE MAIN - Physics (2021 - 27th August Evening Shift - No. 23)
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 $$\sqrt 5 :x$$. The value of x is ___________.
Answer
1
Explanation
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$$\cos \phi = {R \over {\sqrt {{R^2} + 3{R^2}} }}$$
$$ = {1 \over {\sqrt {10} }}$$
$$\cos \phi ' = {R \over {\sqrt {{R^2} + {R^2}} }}$$
$$ = {1 \over {\sqrt 2 }}$$
$${{\cos \phi '} \over {\cos \phi }} = {{\sqrt {10} } \over {\sqrt 2 }} = {{\sqrt 5 } \over 1}$$
$$\therefore$$ x = 1
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