A transmitter transmits at a wavelength of 30 | vedclass

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

Question

(C) The speed of electromagnetic waves is $c = 3 	imes 10^8\ m/s$.The frequency $f$ is given by $f = \frac{c}{\lambda} = \frac{3 	imes 10^8}{300} =

Vedclass · Accepted Answer

$2.5\ nH$

Vedclass · Answer

(C) The speed of electromagnetic waves is $c = 3 	imes 10^8\ m/s$.The frequency $f$ is given by $f = \frac{c}{\lambda} = \frac{3 	imes 10^8}{300} = 10^6\ Hz$.The resonant frequency of an $LC$ circuit is $f = \frac{1}{2 \pi \sqrt{LC}}$.Squaring both sides, we get $f^2 = \frac{1}{4 \pi^2 LC}$.Rearranging for inductance $L$, we get $L = \frac{1}{4 \pi^2 f^2 C}$.Substituting the values: $L = \frac{1}{4 	imes (3.14)^2 	imes (10^6)^2 	imes 9.6 	imes 10^{-6}}$.$L = \frac{1}{4 	imes 9.86 	imes 10^{12} 	imes 9.6 	imes 10^{-6}} = \frac{1}{378.6 	imes 10^6} \approx 2.64 	imes 10^{-9}\ H$.Given the options, the closest value is $2.5\ nH$.

$A$ transmitter transmits at a wavelength of $300\ m$. $A$ capacitor of capacitance $9.6\ \mu F$ is being used. The value of the inductance for the resonant circuit is approximately.

Similar Questions

$A$ charged $30 \mu\text{F}$ capacitor is connected to a $27 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit (in $\text{ rad/s}$)?

The frequency of the output signal of an $LC$ oscillator circuit is $F \ Hz$ with a capacitance of $0.1 \ \mu F$. If the value of the capacitor is increased to $0.2 \ \mu F$,then the frequency of the output signal will be

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is:

Solve the differential equation of $L-C$ circuit and obtain the expression of current.

$A$ charged $30\,\mu F$ capacitor is connected to a $27\,mH$ inductor. The angular frequency of free oscillations of the circuit is

Vedclass Test Series

Exam Paper Generator

Online Exam Module