In a series LCR circuit,C = 2,mu F,L = 1,mH,a | vedclass

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

Question

(A) The current in a series $LCR$ circuit is maximum at the condition of resonance,where the inductive reactance equals the capacitive reactance $(X_L

Vedclass · Accepted Answer

$1 : 1$

Vedclass · Answer

(A) The current in a series $LCR$ circuit is maximum at the condition of resonance,where the inductive reactance equals the capacitive reactance $(X_L = X_C)$.At resonance,the voltage across the inductor $(V_L)$ and the capacitor $(V_C)$ are equal in magnitude but opposite in phase,such that $V_L = V_C = Q \cdot V_{source}$,where $Q$ is the quality factor.The energy stored in the inductor is $U_L = \frac{1}{2} L I_{max}^2$.The energy stored in the capacitor is $U_C = \frac{1}{2} C V_C^2$.At resonance,$I_{max} = \frac{V}{R}$. The voltage across the capacitor is $V_C = I_{max} X_C = \frac{V}{R} \cdot \frac{1}{\omega C}$.Since $\omega = \frac{1}{\sqrt{LC}}$,we have $V_C = \frac{V}{R} \sqrt{\frac{L}{C}}$.Substituting these into the energy expressions:$U_L = \frac{1}{2} L (\frac{V}{R})^2$$U_C = \frac{1}{2} C (\frac{V}{R} \sqrt{\frac{L}{C}})^2 = \frac{1}{2} C \frac{V^2}{R^2} \frac{L}{C} = \frac{1}{2} L \frac{V^2}{R^2}$Thus,$U_C = U_L$,which means the ratio $U_C : U_L = 1 : 1$.

In a series $LCR$ circuit,$C = 2\,\mu F$,$L = 1\,mH$,and $R = 10\,\Omega$. When the current in the circuit is maximum,what is the ratio of the energy stored in the capacitor to the energy stored in the inductor?

Similar Questions

In the circuit shown in the figure, the ratio of the quality factor $(Q)$ to the bandwidth $(\Delta \omega)$ is $.............$ s.

An $LCR$ circuit as shown in the figure is connected to a voltage source $V_{ac}$ whose frequency can be varied. The frequency,at which the voltage across the resistor is maximum,is......$Hz$.

In a series $LCR$ resonant circuit,the quality factor is measured as $100$. If the inductance is increased by two fold and resistance is decreased by two fold,then the quality factor after this change will be .........

An inductor of $0.5 \ mH$,a capacitor of $20 \ \mu F$ and a resistance of $20 \ \Omega$ are connected in series with a $220 \ V$ a.c. source. If the current is in phase with the e.m.f.,the maximum current in the circuit is $\sqrt{x} \ A$. The value of '$x$' is

Vedclass Test Series

Exam Paper Generator

Online Exam Module