For a given series LCR circuit,it is found th | vedclass

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

Question

(B) For maximum current,the circuit must be in resonance.The resonant frequency is given by the formula:$f_0 = \frac{1}{2 \pi \sqrt{L 	imes C}}$Given

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(B) For maximum current,the circuit must be in resonance.The resonant frequency is given by the formula:$f_0 = \frac{1}{2 \pi \sqrt{L 	imes C}}$Given values:$L = 100 \ mH = 100 	imes 10^{-3} \ H = 0.1 \ H$$C = 2.5 \ nF = 2.5 	imes 10^{-9} \ F$Substituting the values into the formula:$f_0 = \frac{1}{2 \pi \sqrt{0.1 	imes 2.5 	imes 10^{-9}}}$$f_0 = \frac{1}{2 \pi \sqrt{25 	imes 10^{-11}}}$$f_0 = \frac{1}{2 \pi \sqrt{2.5 	imes 10^{-10}}}$$f_0 = \frac{1}{2 \pi 	imes 5 	imes 10^{-5}}$Since $\pi^2 = 10$,we have $\pi = \sqrt{10} \approx 3.162$.$f_0 = \frac{1}{2 	imes \sqrt{10} 	imes 5 	imes 10^{-5}} = \frac{1}{10 \sqrt{10} 	imes 10^{-5}} = \frac{10^4}{\sqrt{10}} = \frac{10^4 	imes \sqrt{10}}{10} = 10^3 	imes \sqrt{10} \ Hz$.Wait,let's re-calculate:$f_0 = \frac{1}{2 \pi \sqrt{0.1 	imes 2.5 	imes 10^{-9}}} = \frac{1}{2 \pi \sqrt{2.5 	imes 10^{-10}}} = \frac{1}{2 \pi 	imes 1.581 	imes 10^{-5}} \approx 10000 \ Hz = 10 	imes 10^3 \ Hz$.

Similar Questions

$A$ telephone wire of length $200\, km$ has a capacitance of $0.014\, \mu F$ per km. If it carries an $AC$ of frequency $5\, kHz$,what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum? (in $mH$)

In a series $LCR$ circuit,the frequency of the source is half of the resonance frequency. The nature of the circuit will be:

When resonance is produced in a series $LCR$ circuit,then which of the following is not correct?

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......$Hz$.

The current in resistance $R$ at resonance is

Vedclass Test Series

Exam Paper Generator

Online Exam Module