An oscillating LC circuit consists of a 75,mH | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In an oscillating $LC$ circuit,the total energy is conserved,oscillating between the electric field of the capacitor and the magnetic field of the

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) In an oscillating $LC$ circuit,the total energy is conserved,oscillating between the electric field of the capacitor and the magnetic field of the inductor.The maximum energy stored in the capacitor is equal to the maximum energy stored in the inductor:$\frac{1}{2} L I_{\max}^2 = \frac{1}{2} \frac{Q_{\max}^2}{C}$Rearranging for the maximum current $I_{\max}$:$I_{\max} = Q_{\max} \sqrt{\frac{1}{LC}}$Given values:$L = 75 	imes 10^{-3} \, H$$C = 1.2 	imes 10^{-6} \, F$$Q_{\max} = 2.7 	imes 10^{-6} \, C$Calculating the angular frequency $\omega = \frac{1}{\sqrt{LC}}$:$\omega = \frac{1}{\sqrt{75 	imes 10^{-3} 	imes 1.2 	imes 10^{-6}}} = \frac{1}{\sqrt{90 	imes 10^{-9}}} = \frac{1}{\sqrt{9 	imes 10^{-8}}} = \frac{1}{3 	imes 10^{-4}} = \frac{10^4}{3} \, rad/s$Now,$I_{\max} = Q_{\max} 	imes \omega$:$I_{\max} = (2.7 	imes 10^{-6}) 	imes \frac{10^4}{3} = 0.9 	imes 10^{-2} \, A = 9 	imes 10^{-3} \, A = 9 \, mA$.

An oscillating $LC$ circuit consists of a $75\,mH$ inductor and a $1.2\,\mu F$ capacitor. If the maximum charge on the capacitor is $2.7\,\mu C$,the maximum current in the circuit will be $...........\,mA$.

Similar Questions

$A$ capacitor is fully charged with a battery. Then the battery is removed and a coil is connected with the capacitor in parallel. How does the current vary?

$A$ charged $30\,\mu F$ capacitor is connected to a $27\,mH$ inductor. The angular frequency of free oscillations of the circuit is

The magnetic energy in an inductor changes from maximum value to minimum value in $5 \ ms$. When connected to an $A.C.$ source,the frequency of the source is (in $Hz$)

In the circuit shown below, the switch is kept in position $a$ for a long time and is then thrown to position $b$. The amplitude of the resulting oscillating current is given by

$A$ $LC$ circuit is in the state of resonance. If $C = 0.1 \mu F$ and $L = 0.25 \ H$. Neglecting the ohmic resistance of the circuit,what is the frequency of oscillations in $Hz$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module