For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 and 100 mH inductor are being used in the given circuit.

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Solution

Q.
For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 $Ω$ and 100 mH inductor are being used in the given circuit.

The frequency of ac source is _________ $\times 10^{3}$ Hz. (given $π^{2} = 10$ ) [2024]

Ans.
(10)   For maximum current, circuit must be in resonance.

  At resonance, $X_{C} = X_{L}$

$ω L = \frac{1}{ω C} \Rightarrow ω^{2} = \frac{1}{100 \times 10^{- 3} \times 2.5 \times 10^{- 9}} = 4 \times 10^{9}$

   ${(2 π f)}^{2} = 4 \times 10^{9}$

   $f^{2} = 10^{8} \Rightarrow f = 10^{4} Hz \Rightarrow f = 10 \times 10^{3} Hz$

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