An a.c. e.m.f. of peak value 230 V and frequ | vedclass

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

Question

(A) For the current in an $LCR$ series circuit to be maximum,the circuit must be in resonance.At resonance,the inductive reactance equals the capaciti

Vedclass · Accepted Answer

$4 \ \mu F, \quad 20 \ A$

Vedclass · Answer

(A) For the current in an $LCR$ series circuit to be maximum,the circuit must be in resonance.At resonance,the inductive reactance equals the capacitive reactance: $X_L = X_C$.Given $L = 2.5 \ H$ and $f = 50 \ Hz$,the inductive reactance is $X_L = 2 \pi f L = 2 \pi (50) (2.5) = 250 \pi \ \Omega$.Using $\pi^2 = 10$,we have $\pi = \sqrt{10} \approx 3.162$,so $X_L = 250 	imes 3.162 = 790.5 \ \Omega$.However,the resonance condition is $X_C = X_L$,so $\frac{1}{2 \pi f C} = 2 \pi f L$.$C = \frac{1}{4 \pi^2 f^2 L} = \frac{1}{4 	imes 10 	imes (50)^2 	imes 2.5} = \frac{1}{40 	imes 2500 	imes 2.5} = \frac{1}{250000} = 4 	imes 10^{-6} \ F = 4 \ \mu F$.At resonance,the impedance $Z = R = 11.5 \ \Omega$.The maximum current $I_{max} = \frac{V_{peak}}{Z} = \frac{230}{11.5} = 20 \ A$.Thus,the values are $4 \ \mu F$ and $20 \ A$.

Similar Questions

The resonant frequency of a circuit is $f$. If the capacitance is made $4$ times the initial value,then the resonant frequency will become

In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \ V$ and $R = 1 \ k\Omega$ with $C = 2 \ \mu F$. The resonant frequency $\omega$ is $200 \ rad/s$. At resonance,the voltage across $L$ is:

In an $LCR$ series circuit at resonance:

In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

An inductor of $0.5\,mH$,a capacitor of $20\,\mu F$ and a resistance of $20\,\Omega$ are connected in series with a $220\,V$ $AC$ source. If the current is in phase with the $EMF$,the amplitude of the current in the circuit is $\sqrt{x}\,A$. The value of $x$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module