A series LCR circuit with inductance 10 H, capacitance , resistance 50 is connected to an AC source of voltage, If the resonant frequency of the LCR circuit is and the frequency of the AC source is , then [2022]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
A series LCR circuit with inductance 10 H, capacitance $10$ $μ F$ , resistance 50 $Ω$ is connected to an AC source of voltage, $V = 200 \sin (100 t) volt .$ If the resonant frequency of the LCR circuit is $υ_{0}$ and the frequency of the AC source is $υ$ , then [2022]

1 $υ_{0} = υ = 50$ $Hz$

2 $υ_{0} = υ = \frac{50}{π}$ $Hz$

3 $υ_{0} = \frac{50}{π} Hz, υ = 50 Hz$

4 $υ = 100$ $Hz, υ_{0} = \frac{100}{π}$ $Hz$

Ans.
(2)

Here, $L = 10$ $H; C = 10$ $μ F; R = 50$ $Ω; V = 200 \sin (100 t)$ $V$

We know that $ω = 2 π υ \Rightarrow υ = \frac{ω}{2 π}$ ...(i)

From eq. (i), $υ = \frac{100}{2 π} = \frac{50}{π} (∵ ω = 100 rad/s)$

$∴$ $Frequency υ = \frac{50}{π} Hz$

At resonance, $υ_{r} = υ_{0} = \frac{1}{2 π \sqrt{L C}}$

$= \frac{1}{2 π \sqrt{10 \times 10 \times 10^{- 6}}} = \frac{1}{2 π \sqrt{10^{- 4}}} = \frac{1}{2 π \times 10^{- 2}} = \frac{100}{2 π} = \frac{50}{π}$ $Hz$

Solution

Q.
A series LCR circuit with inductance 10 H, capacitance $10$ $μ F$ , resistance 50 $Ω$ is connected to an AC source of voltage, $V = 200 \sin (100 t) volt .$ If the resonant frequency of the LCR circuit is $υ_{0}$ and the frequency of the AC source is $υ$ , then [2022]

1 $υ_{0} = υ = 50$ $Hz$

2 $υ_{0} = υ = \frac{50}{π}$ $Hz$

3 $υ_{0} = \frac{50}{π} Hz, υ = 50 Hz$

4 $υ = 100$ $Hz, υ_{0} = \frac{100}{π}$ $Hz$

Want Us to Email you About Special Offers & Updates?

Solution

Q. A series LCR circuit with inductance 10 H, capacitance 10 μF, resistance 50 Ω is connected to an AC source of voltage, V=200sin(100t) volt. If the resonant frequency of the LCR circuit is υ0 and the frequency of the AC source is υ, then [2022]

1 υ0=υ=50Hz

2 υ0=υ=50πHz

3 υ0=50πHz, υ=50Hz

4 υ=100Hz, υ0=100πHz

Ans. (2) Here, L=10H; C=10μF; R=50Ω; V=200sin(100t)V We know that ω=2πυ⇒υ=ω2π ...(i) From eq. (i), υ=1002π=50π (∵ω=100 rad/s) ∴ Frequency υ=50πHz At resonance, υr=υ0=12πLC =12π10×10×10-6=12π10-4=12π×10-2=1002π=50πHz

Want Us to Email you About Special Offers & Updates?

Q.
A series LCR circuit with inductance 10 H, capacitance $10$ $μ F$ , resistance 50 $Ω$ is connected to an AC source of voltage, $V = 200 \sin (100 t) volt .$ If the resonant frequency of the LCR circuit is $υ_{0}$ and the frequency of the AC source is $υ$ , then [2022]

1 $υ_{0} = υ = 50$ $Hz$

2 $υ_{0} = υ = \frac{50}{π}$ $Hz$

3 $υ_{0} = \frac{50}{π} Hz, υ = 50 Hz$

4 $υ = 100$ $Hz, υ_{0} = \frac{100}{π}$ $Hz$