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7.Alternating Current
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Frequency of $L-C$ circuit is $f_{1} .$ If a resistance $R$ is also added to
it, the frequency becomes $f_{2}$. The ratio of $\frac{f_{2}}{f_{1}}$ will be
A
$\sqrt{1+\frac{ R ^{2} C }{4 L }}$
B
$\sqrt{1-\frac{ R ^{2} C }{4 L }}$
C
$\sqrt{1+\frac{ R ^{2} C }{ L }}$
D
$\sqrt{1-\frac{ R ^{2} C }{ L }}$
(AIIMS-2019)
Solution
The frequency $f_{1}$ is given as,
$f _{1}=\frac{1}{\sqrt{ LC }}$
The frequency $f _{2}$ is given as,
$f _{1}=\sqrt{\left(\frac{1}{\sqrt{ LC }}\right)^{2}-\left(\frac{ R }{2 L }\right)^{2}}$
Take the ratio as,
$\frac{ f _{2}}{ f _{1}}=\frac{\sqrt{\left(\frac{1}{\sqrt{ LC }}\right)^{2}-\left(\frac{ R }{2 L }\right)^{2}}}{\frac{1}{\sqrt{ LC }}}$
$=\sqrt{1-\frac{ R ^{2} C }{4 L }}$
Standard 12
Physics
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