In an oscillating L-C circuit in which C = 4.00 $μ F$ , the maximum potential difference across the capacitor during the oscillation is 1.50V and the maximum current through the inductor is $50.0 m A$ . The frequency of the oscillations is $x \times 10 H z$ . Find $x$

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answer is 133.

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Detailed Solution

$a) \frac{1}{2} L i_{0}^{2} = \frac{1}{2} C V_{0}^{2} ∴ L = \frac{C V_{0}^{2}}{i_{0}^{2}} = \frac{(4 \times 10^{- 6}) (1.5)}{{(50 \times 10^{- 3})}^{2}} = 3.6 \times 10^{- 3} H$

$b) f = \frac{1}{2 π \sqrt{2 C}} = \frac{1}{2 π \sqrt{(3.6 \times 10^{- 3}) (4 \times 10^{- 6})}} = 0.133 \times 10^{4} H Z = 1.33 k H Z$

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