In an LC circuit shown in figure C=2μF and L=2μH. At t=0 charge on capacitor is 43 μC and at same instant is increasing at a rate of 6 μC/s.Choose the correct statement(s):

q = q 0 sin ( ω t + π 6 ) i = q 0 ω cos π 6 i = q 0 2 3 2 ⇒ q 0 = 24 3 = 8 3 A l t e r n a t i v e l y q 0 2 2 C = 1 ( 4 3 ) 2 2 + 1 2 × 2 × ( 6 ) 2 q 0 = 8 3 1 2 L i 0 2 = q 0 2 2 C ⇒ i 0 = 4 3

Maximum charge on capacitor is 8 3 μ C

Maximum current through inductor is 4 3 μ A

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In an LC circuit shown in figure $C = 2 μ F a n d L = 2 μ H .$ At t=0 charge on capacitor is $4 \sqrt{3} μ C$ and at same instant is increasing at a rate of $6 μ C / s .$
Choose the correct statement(s):

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Total energy stored in circuit is $24 μ J$

Total energy stored in circuit $48 μ J$

Maximum charge on capacitor is $8 \sqrt{3} μ C$

Maximum current through inductor is $4 \sqrt{3} μ A$

answer is A, B, C.

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Detailed Solution

$q = q_{0} \sin (ω t + \frac{π}{6}) i = q_{0} ω \cos \frac{π}{6} i = \frac{q_{0}}{2} \frac{\sqrt{3}}{2} \Rightarrow q_{0} = \frac{24}{\sqrt{3}} = 8 \sqrt{3} A l t e r n a t i v e l y \frac{q_{0}^{2}}{2 C} = \frac{1 {(4 \sqrt{3})}^{2}}{2} + \frac{1}{2} \times 2 \times {(6)}^{2} q_{0} = 8 \sqrt{3} \frac{1}{2} L i_{0}^{2} = \frac{q_{0}^{2}}{2 C} \Rightarrow i_{0} = 4 \sqrt{3}$

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