An inductor of 0.5 text{ mH}, a capacitor of | vedclass

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

Question

(C) In an $LCR$ series circuit, the current is in phase with the emf when the circuit is in resonance.At resonance, the inductive reactance $X_L$ equa

Vedclass · Accepted Answer

$242$

Vedclass · Answer

(C) In an $LCR$ series circuit, the current is in phase with the emf when the circuit is in resonance.At resonance, the inductive reactance $X_L$ equals the capacitive reactance $X_C$, and the impedance $Z$ of the circuit is equal to the resistance $R$.Given: $R = 20 	ext{ } \Omega$, $V_{rms} = 220 	ext{ V}$.The peak voltage (amplitude of emf) is $V_0 = V_{rms} \sqrt{2} = 220 \sqrt{2} 	ext{ V}$.At resonance, the impedance $Z = R = 20 	ext{ } \Omega$.The amplitude of the current $I_0$ is given by $I_0 = \frac{V_0}{Z} = \frac{220 \sqrt{2}}{20} = 11 \sqrt{2} 	ext{ A}$.We can write $I_0 = \sqrt{11^2 	imes 2} = \sqrt{121 	imes 2} = \sqrt{242} 	ext{ A}$.Comparing this with the given form $[x]^{1/2} 	ext{ A}$, we get $x = 242$.

An inductor of $0.5 \text{ mH}$, a capacitor of $20 \text{ } \mu\text{F}$ and resistance $20 \text{ } \Omega$ are connected in series with a $220 \text{ V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2} \text{ A}$. The value of $x$ is

Similar Questions

In a non-resonant $LCR$ series circuit,what will be the nature of the circuit for frequencies higher than the resonance frequency?

In the given circuit,the readings of voltmeters $V_1$ and $V_2$ are $300 \, V$ each. The readings of voltmeter $V_3$ and ammeter $A$ are respectively:

For the series $LCR$ circuit shown in the figure,what is the resonance angular frequency and the amplitude of the current at the resonating frequency? The source voltage is given as $220 \, V$ ($RMS$ value).

$A$ resistor of resistance $R$, an inductor of inductive reactance $2R$, and a capacitor of capacitive reactance $X_C$ are connected in series to an $A.C.$ source. If the series $LCR$ circuit is in resonance, then the power factor of the circuit and the value $X_C$ are respectively:

What is the sharpness of resonance and obtain an equation for the $Q$ factor?

Vedclass Test Series

Exam Paper Generator

Online Exam Module