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Alternating Current question

2006 · Q129
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Alternating Current question

2006 · Q129

NEETPhysicsAlternating CurrentMCQ+4 / −1
A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency fff. If L is doubled and C is changed to 4C, the frequency will be
  1. A
    f/2f/2f/2
  2. B
    f/4f/4f/4
  3. C
    8f8f8f
  4. D
    f/2f/2f/22\sqrt 22​
View written solutionFree

Correct answer: D

We know that frequency of electrical oscillation in L.C. circuit is

f = 12π1LC{1 \over {2\pi }}\sqrt {{1 \over {LC}}} 2π1​LC1​​

∴\therefore∴ f1f2=(L2C2L1C1)1/2{{{f_1}} \over {{f_2}}} = {\left( {{{{L_2}{C_2}} \over {{L_1}{C_1}}}} \right)^{1/2}}f2​f1​​=(L1​C1​L2​C2​​)1/2

= (2L×4CL×C)1/2=(8)1/2{\left( {{{2L \times 4C} \over {L \times C}}} \right)^{1/2}} = {\left( 8 \right)^{1/2}}(L×C2L×4C​)1/2=(8)1/2

∴\therefore∴ f1f2=22{{{f_1}} \over {{f_2}}} = 2\sqrt 2 f2​f1​​=22​

⇒\Rightarrow⇒ f2=f122{{f_2} = {{{f_1}} \over {2\sqrt 2 }}}f2​=22​f1​​

⇒\Rightarrow⇒ f2=f22{{f_2} = {f \over {2\sqrt 2 }}}f2​=22​f​ [As f1 = f]

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