A source of alternating emf is connected in series with a capacitor and inductor in a circuit with negligible resistance

Question

A source of alternating emf $E = E_{0} \sin ω t$ is connected in series with a capacitor and inductor in a circuit with negligible resistance. Natural frequency of $L C$ oscillation is $ω_{0} = \frac{1}{\sqrt{L C}}$ . If charge on capacitor at any moment is given by $Q = Q_{0} \sin ω t$ then magnitude of $Q_{0}$ is:

Smart Achievers · Accepted Answer

(3)

$E_{0} \sin ω t = \frac{Q}{C} + L \frac{d^{2} Q}{d t^{2}}$

$Putting Q = Q_{0} \sin ω t$

$Q_{0} = \frac{E_{0}}{L (ω^{2} - ω_{0}^{2})}$

Solution

1 $\frac{E_{0}}{| ω^{2} - ω_{0}^{2} |}$

2 $\frac{E_{0}}{L ω^{2}}$

3 $\frac{E_{0}}{L | ω^{2} - ω_{0}^{2} |}$

4 $\frac{E_{0}}{L ω_{0}^{2}}$

Ans.
(3)

$E_{0} \sin ω t = \frac{Q}{C} + L \frac{d^{2} Q}{d t^{2}}$

$Putting Q = Q_{0} \sin ω t$

$Q_{0} = \frac{E_{0}}{L (ω^{2} - ω_{0}^{2})}$

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Solution

Q. A source of alternating emf E=E0sinωt is connected in series with a capacitor and inductor in a circuit with negligible resistance. Natural frequency of LC oscillation is ω0=1LC. If charge on capacitor at any moment is given by Q=Q0sinωt then magnitude of Q0 is:

1 E0|ω2-ω02|

2 E0Lω2

3 E0L|ω2-ω02|

4 E0Lω02